Investigation and Improvement of Thermal Stability of a Chromatic Confocal Probe with a Mode-Locked Femtosecond Laser Source

applied sciences

Article Investigation and Improvement of Thermal Stability of a Chromatic Confocal Probe with a Mode-Locked Femtosecond Laser Source

Ryo Sato, Yuki Shimizu *, Chong Chen, Hiraku Matsukuma and Wei Gao Precision Nanometrology Laboratory, Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan; [email protected] (R.S.); [email protected] (C.C.); [email protected] (H.M.); [email protected] (W.G.) * Correspondence: [email protected]; Tel.: +81-22-795-6950

Received: 6 September 2019; Accepted: 29 September 2019; Published: 30 September 2019

Abstract: An intentional investigation on the thermal stability of a mode-locked femtosecond laser chromatic confocal probe, which is a critical issue for the probe to be applied for long-term displacement measurement or surface profile measurement requiring long-time scanning, is carried out. At first, the thermal instability of the first prototype measurement setup is evaluated in experiments where the existence of a considerably large thermal instability is confirmed. Then the possible reasons for the thermal instability of the measurement setup are analyzed quantitatively, such as the thermal instability of the refractive index of the confocal lens and the thermal expansion of mechanical jigs employed in the probe. It is verified that most of the thermal instability of the measurement setup is caused by the thermal expansion of mechanical jigs in the probe. For the improvement of the thermal stability of the probe, it is necessary to employ a low thermal expansion material for the mechanical jigs in the measurement setup and to shorten the optical path length of the laser beam. Based on the analysis result, a second prototype probe is newly designed and constructed. The improved thermal stability of the second prototype probe is verified through theoretical calculations and experiments.

Keywords: chromatic confocal probe; thermal stability; measurement resolution; mode-locked femtosecond laser

1. Introduction Confocal microscopes [1,2] are valuable instruments for non-contact surface profile measurement [3,4], and are employed in various scientific and industrial fields due to their principles that allow three-dimensional profile measurement in the ambient atmosphere. One of the main features of the confocal probe employed in a confocal microscope is a depth-sectioning effect that realizes a high resolution measurement in the axial direction by extracting a signal from the focal plane while excluding the unnecessary signals from the other planes [5]. In the case of a confocal probe employing a monochromatic light source [6–9], it is necessary to scan a target sample in the axial direction for obtaining an axial response; the maximum signal of the axial response is reached when the surface is exactly located on the focal plane of the objective lens in the confocal probe [9]. Meanwhile, in the case of a confocal probe employing a chromatic light source and a chromatic objective lens, which is often referred to as the chromatic confocal probe [9–12], the height information can be obtained by monitoring the light spectrum detected by the point detector in the confocal probe. In a chromatic confocal probe, the axial chromatism is used as a space-coding method, in which a different wavelength is associated with each point of the optical axis to provide a mathematical relationship between the surface height and the wavelength focused on the surface [9]; namely, the height information can be obtained without scanning the target in the axial direction. This characteristic allows the chromatic

Appl. Sci. 2019, 9, 4084; doi:10.3390/app9194084 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 4084 2 of 17 confocal probe to reduce the influences of motion errors of the mechanical scan of a target sample. Conventional chromatic confocal probes employing a white light source such as a halogen lamp or an LED (light-emitting diode) have been achieved a sub-micrometric vertical resolution [13–16]. Meanwhile, instability and low spectral power density of such a white light source are issues to be addressed to achieve better performances. In responding to the background described above, several types of chromatic confocal probes employing a super-continuum light source, which has a higher light intensity, better spatial coherence, and a wider spectral range, have been developed so far [17–20]. In addition, optical configurations with various dual-detector setups have been proposed to obtain axial responses in a better sensitivity [21–24]. The author’s group has also proposed a chromatic confocal probe with a new dual-detector setup and a mode-locked femtosecond laser source [24]. The proposed femtosecond laser chromatic confocal probe is designed to divide the reflected laser beam from a target sample surface into two beams and capture them by two identical fiber detectors of an optical spectrum analyzer. It should be noted that one of the divided beams is coupled into the fiber detector placed on the focal plane of a coupling lens, while the other beam is coupled into another fiber detector placed on the plane slightly shifted from the focal plane of another coupling lens; namely, the optical setup has two different confocal setups. By obtaining light spectra of the divided beams captured in the different confocal setups, the “normalized” spectrum, which can be employed as a highly-sensitive axial response, can be obtained [24]. Experimental results have demonstrated that the proposed method can realize a vertical resolution of 30 nm and a measurement range of 40 µm [24]. Furthermore, it has also been demonstrated that the measurement range can be expanded to 250 µm by utilizing side-lobes in the normalized spectrum [25]. On the other hand, since an optical spectrum analyzer is employed to read the spectra over a wide light wavelength range of 160 nm in the developed setup, it takes a relatively long time (8 s) to make the measurement at one height position of a target sample. The thermal stability of the probe is thus a critical issue when the developed probe is applied for long-term displacement measurement or surface profile measurement where long-time scanning is required. In this paper, experimental verification of the thermal stability of the first prototype femtosecond laser chromatic confocal probe [24] is carried out where a considerably large thermal instability of the probe for displacement measurement is verified. The possible reasons for the thermal instability of the probe, such as the thermal instability of the refractive index of the confocal lens and the thermal expansion of mechanical jigs of the probe, are then analyzed quantitatively. Based on the analysis results, a second prototype femtosecond laser chromatic confocal probe is newly designed and constructed to improve the thermal stability for displacement measurement where the optical path length of the laser beam is minimized and a low thermal expansion material is employed for mechanical jigs in the optical setup. Experimental results for demonstrating the improved thermal stability of the second prototype probe are also presented. It should be noted that the thermal stability of the overall chromatic confocal measurement setup is contributed by not only the thermal stability of the chromatic confocal probe itself but also the thermal stabilities of the sample, the sample jigs, and the mounting plate. This paper is focused on the thermal stability of the chromatic confocal probe since the thermal stabilities of the sample, the sample jigs, and the mounting plate change when the probe is employed for different applications.

2. Thermal Stability of the Chromatic Confocal Measurement Setup

2.1. Principle of the Femtosecond Laser Chromatic Confocal Probe A schematic of the design of the overall chromatic confocal measurement setup, which is referred to as the first prototype measurement setup, is shown in Figure1. The setup is composed of a mode-locked femtosecond laser chromatic confocal probe, which is referred to as the first prototype probe, a sample unit composed of the sample and the sample jigs, and the mounting plate on which the probe and the sample unit are placed. A photograph of the setup is shown in Figure2. Figure2a shows the Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 18 Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 18 prototype probe, a sample unit composed of the sample and the sample jigs, and the mounting prototype probe, a sample unit composed of the sample and the sample jigs, and the mounting plate on which the probe and the sample unit are placed. A photograph of the setup is shown in Appl.plate Sci. on2019 which, 9, 4084 the probe and the sample unit are placed. A photograph of the setup is shown3 of in 17 Figure 2. Figure 2a shows the photograph of the overall first prototype measurement setup, and Figure 2. Figure 2a shows the photograph of the overall first prototype measurement setup, and Figure 2b shows the sample unit. The probe and the sample unit are placed on the mounting plate Figure 2b shows the sample unit. The probe and the sample unit are placed on the mounting plate photographmade of stainless of the steel. overall first prototype measurement setup, and Figure2b shows the sample unit. made of stainless steel. The probe and the sample unit are placed on the mounting plate made of stainless steel.

Figure 1. A schematic of the first prototype chromatic confocal measurement setup. Figure 1. A schematic of the first ﬁrst prototype ch chromaticromatic confocal measurement setup.

Figure 2.2. PhotographPhotograph ofof thethe firstfirst prototype prototype chromatic chromatic confocal confocal measurement measurement setup: setup: (a )(a Photograph) Photograph of Figure 2. Photograph of the first prototype chromaticb confocal measurement setup: (a) Photograph theof the overall overall chromatic chromatic confocal confocal measurement measurement setup; setup; ( )(b Photograph) Photograph of theof the sample sample unit unit composed composed of aof sample the overall and samplechromatic jigs. confocal (CL: Collimating measurement lens, setup; BS: Beam (b) splitter,Photograph PBS: Polarizedof the sample beam unit splitter, composed QWP: of a sample and sample jigs. (CL: Collimating lens, BS: Beam splitter, PBS: Polarized beam splitter, Quarter-waveof a sample and plate, sample L1 and jigs. L2: (CL: Fiber Collimating coupling lenses).lens, BS: Beam splitter, PBS: Polarized beam splitter, QWP: Quarter-wave plate, L1 and L2: Fiber coupling lenses). QWP: Quarter-wave plate, L1 and L2: Fiber coupling lenses). Figure3 shows the principle of the proposed femtosecond laser chromatic confocal probe [ 24,25]. Figure 3 shows the principle of the proposed femtosecond laser chromatic confocal probe In theFigure probe, 3 a mode-lockedshows the principle femtosecond of the laser proposed source is femtosecond employed as thelaser light chromatic source. Theconfocal wavelength probe [24,25]. In the probe, a mode-locked femtosecond laser source is employed as the light source. The of[24,25].ith mode In theλi probe,in a mode-locked a mode-locked femtosecond femtosecond laser la isser well source known is employed to be expressed as the light by the source. following The wavelength of ith mode λi in a mode-locked femtosecond laser is well known to be expressed by the equationwavelength [26 –of28 ith]: mode λi in a mode-locked femtosecond laser is well known to be expressed by the following equation [26–28]: c following equation [26–28]: λi = (1) iνrep + νCEO = c λ c (1) where c is the speed of light, νrep is the pulseλi = repetition+ rate, and νCEO is the carrier envelope i iννrep+ CEO (1) offset frequency. The femtosecond laser beam fromiννrep the CEO laser source (MenloSystems Inc., Germany, C-Fiber-SYNC100) with an average output power of 30 mW was transmitted to the optical setup by a single-mode fiber. A pulse repetition rate of the femtosecond laser was set to be 100 MHz. A spectral Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 18

where c is the speed of light, νrep is the pulse repetition rate, and νCEO is the carrier envelope offset frequency. The femtosecond laser beam from the laser source (MenloSystems Inc., Germany, Appl. Sci. 2019, 9, 4084 4 of 17 C-Fiber-SYNC100) with an average output power of 30 mW was transmitted to the optical setup by a single-mode fiber. A pulse repetition rate of the femtosecond laser was set to be 100 MHz. A bandwidthspectral bandwidth of the femtosecond of the femtosecond laser ranged laser from ranged 1480 from nm to 1480 1640 nm nm. to The 1640 femtosecond nm. The femtosecond laser beam fromlaser thebeam ﬁber from is collimated the fiber by is a collimatingcollimated lensby (CL),a collimating and is made lens incident (CL), and to a chromaticis made objectiveincident lensto a afterchromatic passing objective through lens a polarized after passing beam splitterthrough (PBS) a polarized and a quarter-wave beam splitter plate (PBS) (QWP). and Aa plano-convexquarter-wave lensplate made (QWP). of N-SF11A plano-convex is employed lens as made the chromatic of N-SF11 objective is employed lens. as Due the tochromatic the chromatic objective aberration lens. Due of theto the chromatic chromatic objective aberration lens of employed the chromatic in the objectiv probe, eache lens mode employed in the in collimated the probe, femtosecond each mode in laser the beamcollimated is focused femtosecond on a diﬀ lasererent beam focal is plane focused of the on lens. a different The focal focal length planefλ ofi of the the lens. chromatic The focal objective length lensfλi of corresponding the chromatic objective to the ith lens mode corresponding is expressed as tofollows: the ith mode is expressed as follows:

= 1 1 f f=λ (2) λi i ()−− () (2) nλnRRλ 1 11(1/R//1 121/ 1R2) i −i − wherewhere RR11 andand RR22 represent the curvaturecurvature radiiradii ofof thethe chromaticchromatic objectiveobjective lenslens [[29],29], andand nnλλii isis thethe refractiverefractive indexindex ofof thethe lenslens materialmaterial thatthat cancan bebe expressedexpressed byby thethe followingfollowing equation:equation:

s 222 B123λ2 B λ2 B λ 2 n =+1 B1λi iii +B2λi +B3λi (3) n =λi 1 + 22+ + 2 (3) λi 2 −−−2 2 λλiiCC123λλ CC λ iC i − 1 i − 2 i − 3

k k wherewhere BBk andand CCk ((k = 1, 2, 3) are thethe parametersparameters inherentinherent toto thethe lenslens materialmaterial [[30].30]. TheThe relationshiprelationship between λi and fλi can therefore be uniquely identified by Equation (2). The laser beam reflected between λi and fλi can therefore be uniquely identified by Equation (2). The laser beam reflected fromfrom thethe flatflat mirrormirror surfacesurface passespasses thethe chromaticchromatic objectiveobjective lenslens andand thethe PBSPBS again,again, andand isis reflectedreflected byby thethe PBS.PBS. AfterAfter that, the laser beam is splitsplit intointo twotwo sub-beamssub-beams (the(the measurementmeasurement beambeam andand thethe referencereference beam)beam) by by a beama beam splitter splitter (BS). (BS). In the In probe, the probe, a pair ofa identicalpair of identical single-mode single-mode fibers is employed fibers is asemployed point detectors. as point Thedetectors. measurement The measurement beam is coupled beam is into coupled one of into the one single-mode of the single-mode fibers by usingfibers aby fiber using coupling a fiber lens coupling (L1), while lens (L1), the reference while the beam reference is coupled beam into is thecoupled other into single-mode the other fiber single-mode by using anotherfiber by fiber using coupling another lens fiber (L2). coupling It should lens be (L2). noted It that should one ofbe the noted fiber that detectors one of (Detector1) the fiber detectors is placed at(Detector1) the focal plane is placed of L1, at while the foca thel other plane (Detector2) of L1, while is placed the other at the (Det positionector2) with is placed a defocus at thed (, position0) from thewith focal a defocus plane of d L2.(≠0) The from sub-beams the focal areplane then of transmitted L2. The sub-beams to an optical are spectrumthen transmitted analyzer to through an optical the single-modespectrum analyzer fibers to through obtain thethe opticalsingle-mode spectra fibers of the to measurement obtain the optical beam spectraImea and of the the reference measurement beam beam Imea and the reference beam Iref, and then the normalized axial response In is analyzed. Iref, and then the normalized axial response In is analyzed.

Figure 3. Figure 3.Principle Principle of of the the mode-locked mode-locked femtosecond femtosecond laser la chromaticser chromatic confocal confocal probe (BS:probe Beam (BS: splitter, Beam PBS: Polarized beam splitter, QWP: Quarter-wave plate, L1 and L2: Fiber coupling lenses). splitter, PBS: Polarized beam splitter, QWP: Quarter-wave plate, L1 and L2: Fiber coupling lenses). Appl. Sci. 2019, 9, 4084 5 of 17

In the proposed chromatic confocal probe, a ﬁber-based dual-detector is introduced to eliminate the inﬂuence of the non-smooth spectrum of the mode-locked laser source [20,24]. Based on the spectra Imea and Iref obtained by Detector1 and Detector2, respectively, a normalized axial response In expressed by the following equation can be obtained:

Imea In = (4) Iref

Figure4a shows an example of the spectra obtained by the pair of single-mode fibers. Each of the obtained spectra (Imea and Iref) is the consequence of the convolution of the axial response of the confocal setup and the spectrum of the light source. It should be noted that the influences of the reflectance of the target surface as well as the transmittances of optical components in the setup also influence the obtained spectra. Since the femtosecond laser source has the non-uniform spectrum, the obtained spectra Imea and Iref also become non-uniform. This means that it is difficult to directly extract the peaks in the light spectra, which are required to obtain the axial position information of a measurement target surface under inspection. Meanwhile, by introducing the normalized axial response In expressed by Equation (4), the influences of the non-uniformity in the spectrum of the light source as well as the surface reflectance can be canceled through the normalization process. Furthermore, by employing identical fiber coupling lenses and single-mode fibers for obtaining both Imea and Iref, influences of the transmittances of these optical components can also be minimized through the normalization process. Figure4b shows the normalized axial response In obtained by Imea and Iref shown in Figure4a. As can be seen in this figure, the valley in Iref is detected as the peak in the normalized axial response. It should be noted that the peak in the normalized axial response is sharper than those in Imea and Iref. In the confocal system, the sharper peak in the axial response contributes to the realization of higher accuracy in identifying the focused wavelength λfocused, and hence the higher resolution in measurement of the axial displacement. Figure5 shows the procedure of how to obtain the axial position information of the measurement target surface under inspection from the normalized axial response. Figure5a shows the normalized axial response In. The wavelength λfocused at the peak in the normalized axial response, which is referred to as the focused wavelength, can be obtained by the following equation: P (In(λi) λi) λ focused = P × (5) In(λi)

Figure5b shows a schematic of the relationship between the focused wavelength λfocused and the Z position information of the measurement target surface. The Z displacement of the target sample surface can be calculated by the following equation:

dZ ∆Z = ∆λ (6) dλ · focused where dZ/dλ corresponds to the Z displacement detection sensitivity with respect to the change in the focused wavelength λfocused. The sensitivity dZ/dλ can be theoretically calculated, since the relationship between the focal length fλi of the chromatic objective lens and the corresponding light wavelength λi can be calculated based on Equations (2) and (3). According to the speciﬁcation of the chromatic objective lens employed in the ﬁrst prototype confocal probe (the details of which can be found in Reference [24]), fi-λi sensitivity (df/dλ) is calculated to be 255 nm/nm. It should be noted that the positive direction of the Z displacement of the target sample surface is set as the direction the sample approaches the chromatic objective lens; namely, df/dλ = ( dZ/dλ). The sensitivity dZ/dλ is therefore − calculated to be 255 nm/nm. − Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 18 Appl. Sci. 2019, 9, 4084 6 of 17 Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 18

Figure 4. Schematics of detected spectra by a fiber-based dual-detector. (a) An example of the Figure 4. Schematics of detected spectra by a ﬁber-based dual-detector. (a) An example of the spectra spectraFigure 4. obtained Schematics by the of detectedpair of single-mode spectra by a fibers; fiber-based (b) The dual-detector. normalized axial (a) An response example curve of the In obtained by the pair of single-mode ﬁbers; (b) The normalized axial response curve In obtained by Imea obtainedspectra obtained by Imea and by Iref the shown pair in of ( single-modea). fibers; (b) The normalized axial response curve In and Iref shown in (a). obtained by Imea and Iref shown in (a).

Applies to intensity above threshold Applies to intensity  above threshold  focused

Noise focused intensity

Normalized Normalized Noise Wavelength intensity Normalized Normalized Wavelength focused Z

Wavelengthfocused  ZZdisplacement Focused wavelengthWavelength  Z displacementZ displacement Focused wavelength Z displacement In i  i  dZ focused  Z  focused InIi   i  ddZ    n i Z   focused I  d focused  n i  Z- dZ I   is intensity of  255 nm/nm n i i sensitivityZ- ddZ I   is intensity of  255 nm/nm n i i sensitivity d (b) : Z- sensitivity (a) : Normalized axial response In (b) : Z- sensitivity (a) : Normalized axial response In Figure 5. Principle of a method to obtain the Z displacement from the normalized axial response I Figure 5. Principle of a method to obtain the Z displacement from the normalized axial response nIn and Z-λ sensitivity: (a) Focused wavelength extracted from the normalized axial response In;(b) Z andFigure Z-λ 5. sensitivity: Principle of (a a) Focusedmethod towavelength obtain the extractedZ displacement from the from normalized the normalized axial response axial response In; (b) IZn displacement calculated by using the Z-λ sensitivity. displacementand Z-λ sensitivity: calculated (a) Focused by using wavelength the Z-λ sensitivity. extracted from the normalized axial response In; (b) Z displacement calculated by using the Z-λ sensitivity. Experimental results have demonstrated that the first prototype confocal probe has an axial Experimental results have demonstrated that the first prototype confocal probe has an axial resolution of 30 nm [24]. Since the fiber-based dual-detector normalization method makes it possible to resolutionExperimental of 30 nm results [24]. Since have the demonstrated fiber-based dual-detector that the first normalization prototype confocal method probe makes has it possible an axial measure the axial displacement without the influence of the non-uniform spectrum of the light source, toresolution measure of the 30 axialnm [24]. displacement Since the fiber-based without the dual-detector influence of normalization the non-uniform method spectrum makes of it thepossible light an axial displacement measurement range of 40 µm has been realized by fully utilizing a spectral range source,to measure an axialthe axial displacement displacement measurement without the range influence of 40 μmof the has non-uniform been realized spectrum by fully of utilizing the light a of 160 nm of the femtosecond laser [24]. The displacement measurement is also not influenced by the spectralsource, anrange axial of displacement 160 nm of the measurement femtosecond rangelaser [24].of 40 The μm displacement has been realized measurement by fully isutilizing also not a surface reflectance of the target sample, as well as the transmittance of optical components in the probe. influencedspectral range by theof 160 surface nm of reflectance the femtosecond of the targetlaser [24].sample, The asdisplacement well as the measurementtransmittance isof also optical not componentsinfluenced by in thethe surfaceprobe. reflectance of the target sample, as well as the transmittance of optical components in the probe. Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 18

Appl. Sci.On 2019the, other9, 4084 hand, due to the slow measurement throughput of the optical spectrum analyzer,7 of 17 it takes quite a long time (approximately 8 s) to take the spectra Imea and Iref at a position in a sample plane. Good thermal stability of the probe is thus required to apply the probe for long-term On the other hand, due to the slow measurement throughput of the optical spectrum analyzer, displacement measurement or surface profile measurement with multi-point scanning. For this it takes quite a long time (approximately 8 s) to take the spectra I and I at a position in a sample purpose, it is important to identify the thermal stability ofmea the developedref probe in axial plane. Good thermal stability of the probe is thus required to apply the probe for long-term displacement displacement measurement. It should be noted that the thermal stability of the overall chromatic measurement or surface profile measurement with multi-point scanning. For this purpose, it is important confocal measurement setup is contributed by not only the thermal stability of the chromatic to identify the thermal stability of the developed probe in axial displacement measurement. It should confocal probe itself but also the thermal stability of the sample, the sample jig, and the mounting be noted that the thermal stability of the overall chromatic confocal measurement setup is contributed plate (Figure 1). From the point of view of the developed femtosecond laser chromatic confocal by not only the thermal stability of the chromatic confocal probe itself but also the thermal stability of probe, it is necessary to separate the thermal stability of the probe from those of the sample, the the sample, the sample jig, and the mounting plate (Figure1). From the point of view of the developed sample jig, and the mounting plate. Since it is difficult to directly measure the thermal stability of femtosecond laser chromatic confocal probe, it is necessary to separate the thermal stability of the the probe, in the rest of this section, the thermal stability of the overall measurement setup shown probe from those of the sample, the sample jig, and the mounting plate. Since it is difficult to directly in Figure 1 is measured first. Then an analytical work is carried out in the next section to measure the thermal stability of the probe, in the rest of this section, the thermal stability of the overall characterize the thermal stability of the first prototype probe. measurement setup shown in Figure1 is measured first. Then an analytical work is carried out in the 2.2.next Experimental section to characterize Verification theof the thermal Thermal stability Stability of of the the first Overall prototype Chromatic probe. Confocal Measurement Setup 2.2. Experimental Verification of the Thermal Stability of the Overall Chromatic Confocal Measurement Setup It is difficult to directly obtain the thermal stability of the overall measurement setup for axial It is difficult to directly obtain the thermal stability of the overall measurement setup for axial displacement measurement (dZ/dT). Meanwhile, the Z-λ sensitivity (dZ/dλ) can be theoretically displacement measurement (dZ/dT). Meanwhile, the Z-λ sensitivity (dZ/dλ) can be theoretically calculated as described above. Therefore, by obtaining the thermal stability of the detection of calculated as described above. Therefore, by obtaining the thermal stability of the detection of focused focused wavelength (dλ/dT) in experiments, dZ/dT can be calculated from the following equation: wavelength (dλ/dT) in experiments, dZ/dT can be calculated from the following equation: dZ dλ dZ dZ dλ dZ  (7) = (7) dTdTdT dT· dλ dλ To obtain obtain the the thermal thermal stability stability of of the the detection detection of focusedof focused wavelength wavelength (dλ/ dT (dλ/dT), experiments), experiments were werecarried carried out by out using by using the setup the setup shown shown in Figure in Figure2. A flat 2. mirror,A flat mirror, which which was employed was employed as the targetas the focused targetsample, sample, was held was stationary held stationary in the in setup the setup while while a variation a variation of the of focused the focused wavelength wavelengthλfocused λ was wasobserved observed at each at 100each s over100 s a over period a ofperiod 5000 of s. As5000 can s. be As seen can in be Figure seen 2inb, aFigure temperature 2b, a temperature sensor was sensorplaced was in the placed optical in setupthe optical to monitor setup theto temperaturemonitor the temperature deviation. Figure deviation.6 shows Figure the result6 shows of thethe result of the thermal stability of the detection of focused wavelength λfocused contributed by not only thermal stability of the detection of focused wavelength λfocused contributed by not only the thermal thestability thermal of the stability chromatic of theconfocal chromatic probe itselfconfocal but also probe the itself thermal but stability also the of thermal the sample stability unit and of the samplemounting unit plate. and It the should mounting be noted plate. that It experiments should be noted were that carried experiments out in a laboratory were carried room out whose in a laboratory room whose temperature was controlled to be 20 °C ± 0.5 °C, while the temperature temperature was controlled to be 20 ◦C 0.5 ◦C, while the temperature periodically deviated in a few periodically deviated in a few hours. As± can be seen in the figure, a clear correlation can be found hours. As can be seen in the figure, a clear correlation can be found between the variation of λfocused betweenand the changethe variation in temperature. of λfocused and Three the repetitivechange in experiments temperature. were Three carried repetitive out, andexperiments a mean valuewere carriedof dλ/dT out,was and evaluated a mean tovalue be of20.4 dλ nm/dT/ wasC. Therefore, evaluated fromto be Equation −20.4 nm/°C. (7),the Therefore, thermal from stability Equation of the − ◦ (7),overall the measurement thermal stability setup of for theaxial overall displacement measurement measurement setup for (axialdZ/dT displacement) was evaluated measurement as dZ/dT = (dZ/dT20.4) nm was/ C) evaluated( 255 nm as/nm) dZ/dT= 5.20= (−20.4µm /nm/°C)·(−255C. nm/nm) = 5.20 μm/°C. − ◦ · − ◦ 1550 20.0

T ˚C T 1545 19.8 nm focused 1540 19.6 focused d  -T Sensitivity: 20.2 nm/癈 dT Temperature

Focused wavelength Focused 1535 19.4 0 1000 2000 3000 4000 5000 Time s

Figure 6. The thermal stability of the focused wavelength λfocused of the overall measurement setup Figure 6. The thermal stability of the focused wavelength λfocused of the overall measurement setup evaluated in the experiment by the setup shown in Figure2. evaluated in the experiment by the setup shown in Figure 2. Appl. Sci. 2019, 9, 4084 8 of 17

This result means that a temperature variation in the laboratory room ranging from 19.5 ◦C to 20.5 C could result in a deviation of the detected axial displacement of 2.60 µm in the overall ◦ ± chromatic confocal measurement setup. Regarding long-term displacement measurement or surface proﬁle measurement where long-time scanning is required, the thermal stability of the developed chromatic confocal probe needs to be improved. A detailed investigation is therefore carried out in the following section to separate and characterize the thermal stability of the femtosecond laser chromatic confocal probe based on the measurement result of the overall measurement setup in Figure6.

3. Characterization of the Thermal Stability of the Femtosecond Laser Chromatic Confocal Probe The possible factors contributing to the thermal stability of the overall measurement setup are shown in Table1. The contribution of each factor is analyzed for characterizing the thermal stability of the probe itself.

Table 1. Possible factors contributing to the thermal stability of the overall measurement setup.

Item Factor Symbol

Refractive index instability of the chromatic objective lens P1 = (dZ/dT)P1 Refractive index instability of the surrounding air P2 = (dZ/dT)P2 Probe Thermal expansion of mechanical jigs P3 = (dZ/dT)P3 Thermal expansion of optical path length P4 = (dZ/dT)P4 P = (dZ/dT) Thermal stability of the probe Probe = P1 + P2 + P3 + P4

Thermal expansion of the sample S1 Sample unit Thermal expansion of the sample jig S2 S = (dZ/dT) Thermal stability of the sample unit Sample unit = S1 + S2 Thermal expansion of the mounting plate (corresponding to Mounting plate M = (dZ/dT) the thermal stability of the mounting plate) Mounting plate O = (dZ/dT) Thermal stability of the overall setup Overall = P + S + M

(a) Contribution of the refractive index instability of the chromatic objective lens (P1) The relationship between the refractive index of a lens placed in a vacuum and the temperature T0 (reference temperature @20 ◦C) is described by the following equation [31,32]:

2   dn (λi, T) n (λi, T0) 1 E + 2E ∆T  abs = − D + 2D ∆T + 3D ∆T2 + 0 1  (8)  0 1 2 2  dT 2n(λi, T0)  λ 2 λ  i − iTK where ∆T (=T T ) is temperature deviation from a reference temperature T , and Dp (p = 0, 1, 2), − 0 0 Eq (q = 0, 1) and λTK are the parameters inherent to the lens material. The physical parameters associated with the employed chromatic objective lens in this paper are presented in Table2[ 32]. Based on Equation (8), refractive index instability is calculated to be 1.0629 10 6 C 1 at λ = 1560 nm; − × − ◦ − i this value corresponds to thermal instability of the focused wavelength dλ/dT of 0.0594 nm/◦C from Equation (3). Therefore, the contribution of the refractive index instability of the chromatic objective lens in the thermal stability of the probe is calculated as P = (0.0594 nm/ C) ( 255 nm/nm) = 15.1 nm/ C 1 ◦ · − − ◦ from Equation (7). Appl. Sci. 2019, 9, 4084 9 of 17

Table 2. The physical parameters of N-SF11 employed in the theoretical calculations [32].

Symbol Value D 3.56 10 6 0 − × − D 9.20 10 9 1 × − D 2.10 10 11 2 − × − E 9.65 10 7 0 × − E 1.44 10 9 1 × − λTK 0.294

(b) Contribution of the refractive index instability of the surrounding air (P2)

When the air refractive index nair and the lens refractive index nlens are deﬁned, Equation (2) can be rewritten as follows: 1 f = (9) λi (n /n 1)(1/R 1/R ) lens air − 1 − 2 Diﬀerentiating f λ1 with respect to nair gives the following equation:

d f 1 n = lens 2 2 dnair (n /n 1) (1/R 1/R ) nair lens n air − 1 − 2 (10) = lens f n (n n ) · air lens − air Modifying the above equation gives the following equation: ! d f n dn dZ = lens f air = (11) dT n (n n ) · · dT − dT air lens − air

Here, the air refractive indices of the lens (nlens) and the air (nair) at the reference temperature are 1.7432 (at λ = 1560 nm) and 1.00027, respectively. According to Ciddor’s theoretical formula [33], the refractive index instability of the air (dn /dT) is approximately 1.0 10 6/ C. Therefore, air − × − ◦ from Equation (11), the contribution of the refractive index instability of the surrounding air in the thermal stability of the probe is calculated as P = 24.7 nm/ C at λ = 1560 nm. 2 − ◦ (c) Contributions of the thermal expansion of mechanical jigs (P3) and the mounting plate (M) Figure7 shows a detailed schematic of the chromatic confocal lens and the target sample in the measurement setup shown in Figure2b. Now we consider the variation of the distance between the target sample and the chromatic objective lens in the setup. With the thermal expansion of components in the measurement setup such as the probe, the sample, the sample jig and the mounting plate, the distance between the chromatic objective lens and the sample can be changed. As the ﬁrst step of the research, the thermal expansion of the sample and that of the sample jig are not considered for clarity in the following of this paper, since their contributions to the probe instability are expected to be relatively smaller than that of Jig-B, which is much longer than the other jigs in the probe. It should be noted that the thermal expansion of the sample and that of the sample jig will be taken into consideration for more accurate characterization of thermal stability in future work. In general, the linear thermal expansion of an object can be described by the following equation:

d` = α ` dT (12) · · where d` is the change in the length of the object with the original length `, and α is the linear coeﬃcient of thermal expansion of the object [34]. Here, since the object is expected to expand the same amount in both the directions from its center, |dZ| can be treated to be equal to |d`/2|. From this equation, the contribution of the thermal expansion of a component in the measurement setup can be expressed by the following equation: Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 18 this equation, the contribution of the thermal expansion of a component in the measurement setup canAppl. be Sci. expressed2019, 9, 4084 by the following equation: 10 of 17

dZ dA  A dZ  d`A  αB `A (13) dT= dT = αB 2 (13) dT ± dT ± · 2 wherewhere the subscript subscript A A is isthe the name name of the of component, the component, and the and subscript the subscript B is the kindB is ofthe the kind component of the componentmaterial. Here, material. the Here, sign “the” sign in the “±” equation in the equation is determined is determined by the by location the location of the of objectthe object in thein ± themeasurement measurement setup. setup. When When the the chromatic chromatic objective objectivelens lens approachesapproaches thethe target sample due due to to the the thermalthermal expansion of of the the object, object, the the sign sign is determined is determined as “positive as “positive (+)”. Based (+)”. on Based the above on the equation, above equation,the contributions the contributions of the thermal of the expansion thermal ofexpansion mechanical of jigsmechanical in the probe jigs (inP3 )the and probe the mounting (P3) and plate the mounting(M) are investigated. plate (M) are investigated.

FigureFigure 7. 7. AA detailed detailed schematic schematic of of the the chromatic chromatic confocal confocal lens lens and and the the target target sample sample in in the the chromatic chromatic confocalconfocal measurement measurement setup setup shown shown in in Figure Figure 2b.2b.

At first, the contribution of the thermal expansion of mechanical jigs in the probe (P3) is investigated. At first, the contribution of the thermal expansion of mechanical jigs in the probe (P3) is The main contributor in the mechanical jigs is Jig-B, which connects the lens holder and Jig-A, since its investigated. The main contributor in the mechanical jigs is Jig-B, which connects the lens holder length is the longest among the other jigs in the probe. It should be noted that the influences of other and Jig-A, since its length is the longest among the other jigs in the probe. It should be noted that contributors such as Jig-A or lens holders are not considered at this stage, since the influence of Jig-B the influences of other contributors such as Jig-A or lens holders are not considered at this stage, is dominant. It should also be noted that the influence of the displacement of the flat mirror in the since the influence of Jig-B is dominant. It should also be noted that the influence of the X-direction due to the thermal expansion was expected to be relatively small compared with the main displacement of the flat mirror in the X-direction due to the thermal expansion was expected to be factor regarding a diameter of the focused beam (20 µm) and out-of-flatness of the flat mirror employed relatively small compared with the main factor regarding a diameter of the focused beam (20 μm) in the following experiment (λ/10@633 nm). When the temperature rises, the chromatic objective lens and out-of-flatness of the flat mirror employed in the following experiment (λ/10@633 nm). When approaches the target sample due to the thermal expansion of Jig-B, which is made of aluminum the temperature rises, the chromatic objective lens approaches the target sample due to the thermal having a linear thermal expansion coefficient of 23.1 10 6 C 1 [34] and its line length is designed to expansion of Jig-B, which is made of aluminum having× − a◦ linear− thermal expansion coefficient of be 430 mm. From Equation (13), the contribution of the Jig-B in the thermal stability of the probe is 23.1 × 10−6 °C−1 [34] and its line length is designed to be 430 mm. From Equation (13), the evaluated as P3 = 4.96 µm/◦C. contribution of the Jig-B in the thermal stability of the probe is evaluated as P3 = 4.96 μm/°C. The contribution of the mounting plate M is also investigated. As opposed to the case of Jig-B, The contribution of the mounting plate M is also investigated. As opposed to the case of Jig-B, the chromatic objective lens moves away from the sample due to the thermal expansion of the mounting the chromatic objective lens moves away from the sample due to the thermal expansion of the plate. The mounting plate is made of stainless steel having a linear thermal expansion coefficient of mounting plate. The mounting plate is made of stainless steel having a linear thermal expansion 14.7 10 6 C 1 [34], and its line length is designed to be 100 mm. From Equation (13), the contribution coefficient× − of◦ 14.7− × 10−6 °C−1 [34], and its line length is designed to be 100 mm. From Equation (13), of the mounting plate is therefore calculated as M = (dZ/dT)Mounting plate = 0.735 µm/◦C. the contribution of the mounting plate is therefore calculated as M = (dZ− /dT)Mounting plate = −0.735 μm/°C.(d) Contribution of the thermal expansion of optical path length (P4)

(d) ContributionFigure8 shows of the a schematic thermal expansion of the optical of optical setup inpath the length chromatic (P4) confocal probe. Here, we deﬁne dZ as the axial distance between the focal position of the optical mode with the wavelength λ and λiFigure 8 shows a schematic of the optical setup in the chromatic confocal probe. Here,i+1 we that with the wavelength λi. According to the geometric relationship in the optical setup, the defocus define dZλi as the axial distance between the focal position of the optical mode with the wavelength of the ith optical mode at the ﬁber detector dZλi’ corresponding to dZλi can be expressed by the λi+1 and that with the wavelength λi. According to the geometric relationship in the optical setup, following equation: 2 2F dZλi dZλi0 = (14) 2dZ (L f F) + f 2 λi − λi − λi Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 18

the defocus of the ith optical mode at the fiber detector dZλi’ corresponding to dZλi can be expressed by the following equation:

2F2 dZ Appl. Sci. 2019, 9, 4084   λi 11 of 17 dZλi 2 (14) 2dZLfλi ( λi  F )  f λi wherewhereL Lis is the the distance distance between between the the chromatic chromatic objective objective lens lens and and the the fiber fiber coupling coupling lens, lens, and andF is theF is distancethe distance between between the fiber the fiber coupling coupling lens and lens the and fiber the detector.fiber detector. It should It should be noted be Fnotedcorresponds F corresponds to the focalto the length focal oflength the fiber of the coupling fiber coupling lens. In lens. this paper,In this thepaper, sum the of Lsumand ofF Lis and treated F is totreated be the to optical be the pathoptical length. path In length. the first In prototype the first prototype chromatic confocalchromatic measurement confocal measurement setup, L and setup,F were L designed and F were to be 500 mm and 16.6 mm, respectively. As can be seen in the equation, dZ ’ is affected by L and F, designed to be 500 mm and 16.6 mm, respectively. As can be seen in the λequation,i dZλi’ is affected resulting in the change of the axial response In; namely, the focused wavelength λ is affected by by L and F, resulting in the change of the axial response In; namely, the focused wavelengthfocused λfocused is theaffected thermal by expansionthe thermal of expansion the optical of path the length.optical path length.

X fi L F Y Z fi+1 fi+1 fi D

dZi Zi’

Chromatic Chromatic Fiber objective objective coupling Fiber end face lens Sample lens lens Figure 8. Schematic of the optical setup in the chromatic confocal probe. Figure 8. Schematic of the optical setup in the chromatic confocal probe. However, a theoretical investigation of the contribution of the thermal expansion of optical path However, a theoretical investigation of the contribution of the thermal expansion of optical length (P4) is not an easy task since the equation of the normalized axial response In [24] is quite path length (P4) is not an easy task since the equation of the normalized axial response In [24] is complex. In this paper, experiments were therefore carried out to evaluate P4 quantitatively. At first, quite complex. In this paper, experiments were therefore carried out to evaluate P4 quantitatively. the contribution of the distance F between the fiber coupling lens and the fiber detector in P4 was At first, the contribution of the distance F between the fiber coupling lens and the fiber detector in investigated. The contribution of F in P4 can be calculated from the following equation: P4 was investigated. The contribution of F in P4 can be calculated from the following equation: dZ dF dλ dZ dZ= dF dλ dZ (15) dT dT · dF · dλ  (15) dT dT dF dλ In the above equation, dF/dT and dZ/dλ can be estimated from theoretical calculations. In the first prototypeIn the measurement above equation, setup, dF/dT the fiberand dZ/dλ coupling can lens be estimated and the detector from theoretical were placed calculations. on a jig made In the of aluminumfirst prototype having measurement a linear thermal setup, expansion the fiber coe couplingfficient of lens 23.1 and10 the6 Cdetector1 [34]. Thewere line placed length on of a the jig × − ◦ − jig,made which of aluminum corresponded having to F ,a was linear designed thermal to expansion be 16.6 mm coefficient in the first of prototype 23.1 × 10 measurement−6 °C−1 [34]. The setup. line Fromlength Equation of the (12), jig, which the thermal corresponded expansion to sensitivity F, was designed of the jig dF to/ dT be was 16.6 evaluated mm in the to be first 0.383 prototypeµm/◦C. Inmeasurement addition, dZ/ d setup.λ is already From known Equation as dZ (12),/dλ = the255 thermal nm/nm expansion from the theoretical sensitivity investigation of the jig dF/dT described was − inevaluated the previous to be section 0.383 μm/°C. of this paper.In addition, Meanwhile, dZ/dλ is the already term d knownλ/dF in as Equation dZ/dλ = (15) −255 still nm/nm remains from to bethe addressedtheoretical for investigation the evaluation described of dZ/dT in. the previous section of this paper. Meanwhile, the term dλ/dF in EquationTo obtain (15)dλ /stilldF, experimentsremains to be were addressed carried for out the by evaluation intentionally of dZ changing/dT. F in the measurement setup.To A obtain flat mirror dλ/dF, was experiments employed were as thecarried target out sample, by intentionally and was changing held stationary F in the inmeasurement the setup. Thesetup. experiments A flat mirror were was carried employed out in suchas the a waytarget that sample, the parameter and wasd heldin Figure stationary3, which in correspondedthe setup. The toexperiments the defocus were of Detector2 carried out from in such the focal a way plane that ofthe the parameter fiber coupling d in Figure lens, 3, was which changed corresponded from 0 µm to tothe 300 defocusµm in of a step Detector2 of 20 µ fromm, while the focal the focused plane of wavelength the fiber coupling at each steplens,was wasbeing changed observed. from 0 Inμm the to experiments,300 μm in a thestep deviation of 20 μm, of while the parameter the focusedd (∆ dwavelength) corresponded at each to dFstepin was Equation being (15). observed. It should In the be − notedexperiments, that the positivethe deviation direction of the of theparameter parameter d (Δddwas) corresponded set to be the to one –dF from in Equation the fiberdetector (15). It should to the fiberbe noted coupling that the lens. positive Figure 9directiona shows theof the relationship parameter between d was setd toand be thethe correspondingone from the fiber normalized detector axialto the responses fiber couplingIn obtained lens. in Figure the experiments, 9a shows the and relationship Figure9b shows between the d relationship and the corresponding between d andnormalized the focused axial wavelength responses Inλ focusedobtainedextracted in the experiments, from the normalized and Figure axial 9b responsesshows theI nrelationshipshown in Figurebetween9a. d From and the the experimental focused wavelength results, theλfocused sensitivity extractedd λ from/dF was theevaluated normalized to be axial 0.5686 responses nm/µm. In From Equation (15), the contribution of F in P was therefore evaluated as dZ/dT = (0.383 µm/ C) (0.5686 4 ◦ · nm/µm) ( 255 nm/nm) = 55.5 nm/ C. · − − ◦ Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 18 shownAppl. Sci. in2019 Figure, 9, x FOR 9a. PEER From REVIEW the experimental results, the sensitivity dλ/dF was evaluated to be 0.5686 12 of 18 nm/μm. From Equation (15), the contribution of F in P4 was therefore evaluated as dZ/dT = (0.383 shown in Figure 9a. From the experimental results, the sensitivity dλ/dF was evaluated to be 0.5686 μm/°C)·(0.5686 nm/μm)·(−255 nm/nm) = −55.5 nm/°C. nm/μm. From Equation (15), the contribution of F in P4 was therefore evaluated as dZ/dT = (0.383 Appl. Sci. 2019 9 μm/°C)·(0.5686, , 4084 nm/μm)·(−255 nm/nm) = −55.5 nm/°C. 12 of 17 1640

16001640 R2 = 0.9983 nm 15601600 R2 = 0.9983 nm

focused -d Sensitivity  15201560 -0.5686 nm/mm focused

Focused wavelengthFocused -d Sensitivity  14801520 0 60 -0.5686120 nm/ 180mm 240 300 Focused wavelengthFocused 1480 d displacement mm 0 60 120 180 240 300 d displacement mm

(a) (b)

Figure 9. Relationship(a) between the defocus d and the focused wavelength (b) λfocused: (a) The relationship between d and the obtained normalized axial responses In; (b) The relationship between FigureFigure 9. 9. RelationshipRelationship between between the thedefocus defocusd and d the and focused the wavelength focused wavelengthλfocused:( a)λ Thefocused relationship: (a) The d and the focused wavelength λfocused extracted from the normalized axial responses shown in Figure relationshipbetween d and between the obtained d and the normalized obtained normalized axial responses axial Iresponsesn;(b) The I relationshipn; (b) The relationship between dbetweenand the 9a. dfocused and the wavelength focused wavelengthλfocused extracted λfocused extracted from the from normalized the normalized axial responses axial responses shown in shown Figure in9a. Figure 9a. TheThe contribution contribution of of the the distance distance LL betweenbetween the the chromatic chromatic objective objective lens lens and and the the fiber fiber coupling coupling lens in P4 is also investigated. L (=500 mm) corresponds to the sum of the lengths of the mounting lensThe in P contribution4 is also investigated. of the distanceL (=500 L between mm) corresponds the chromatic to the objective sum of thelens lengths and the of fiber the mountingcoupling plate and Jig-A. To estimate the thermal expansion of L (ΔL), a finite element model (FEM) shown lensplate in and P4 is Jig-A. also investigated. To estimate the L (=500 thermal mm) expansion corresponds of L to(∆ Lthe), asum finite of elementthe lengths model of the (FEM) mounting shown in Figure 10 is employed in this paper. From the result of FEM analysis (by the Autodesk Nastran platein Figure and Jig-A.10 is employed To estimate in the this thermal paper. Fromexpansion the result of L of(ΔL FEM), a finite analysis element (by the model Autodesk (FEM) Nastranshown In-CAD), ΔL is estimated to be approximately 10 μm; this value is small compared with L (=500 inIn-CAD), Figure 10∆L isis employed estimated in to bethis approximately paper. From the 10 µ resultm; this of value FEM isanalysis small compared (by the Autodesk with L (= 500Nastran mm), mm), and the influence of ΔL is negligibly small. From these results, it can be concluded that the In-CAD),and the influence ΔL is estimated of ∆L is negligibly to be approximately small. From these10 μm; results, this value it can beis small concluded compared that the with contribution L (=500 contribution of F is much larger than that of L in the contribution of the thermal expansion of mm),of F is and much the larger influence than thatof Δ ofL isL innegligibly the contribution small. From of the these thermal results, expansion it can of be optical concluded path lengththat theP4 . optical path length P4. As a result, P4 was evaluated to be −55.5 nm/°C. It should be noted that the contributionAs a result, P of4 wasF is evaluated much larger to be than55.5 that nm of/◦ C.L inIt should the contribution be notedthat of the the thermaluncertainty expansion of L could of uncertainty of L could increase the −measurement uncertainty of the femtosecond laser chromatic opticalincrease path the length measurement P4. As a uncertainty result, P4 was of the evaluated femtosecond to be laser−55.5 chromatic nm/°C. It confocalshould be probe. noted Therefore, that the confocal probe. Therefore, the optical path length L is expected to be reduced for the stabilization of uncertaintythe optical path of L lengthcould Lincreaseis expected the measurement to be reduced foruncertainty the stabilization of the femtosecond of the femtosecond laser chromatic chromatic the femtosecond chromatic confocal probe. confocalconfocal probe. probe. Therefore, the optical path length L is expected to be reduced for the stabilization of the femtosecond chromatic confocal probe.

Figure 10. Thermal expansion of each component estimated in the simulation based on a finite Figureelement 10. model. Thermal expansion of each component estimated in the simulation based on a finite element model. Figure 10. Thermal expansion of each component estimated in the simulation based on a finite Table3 summarizes the contribution of each factor on the overall thermal stability of the setup. element model. In summary,Table 3 summarizes the thermal the stability contribution of the overall of each measurement factor on the overall setup ( dZthermal/dT)Overall stabilityis evaluated of the setup. to be In4.13 summary,µm/ C from the thermal the theoretical stability investigation. of the overall A measurement difference of approximatelysetup (dZ/dT)Overall 1 µ mis/ evaluatedC can be foundto be Table◦ 3 summarizes the contribution of each factor on the overall thermal stability◦ of the setup. 4.13between μm/°C the from thermal the theoretical stability estimated investigation. in theory A difference (4.13 µm /of◦C) approximately and that obtained 1 μm/°C in the can experiments be found In summary, the thermal stability of the overall measurement setup (dZ/dT)Overall is evaluated to be (5.20 µm/ C) described in the previous section of this paper; the difference is considered to be the 4.13 μm/°C◦ from the theoretical investigation. A difference of approximately 1 μm/°C can be found sum of the small contributions from the other factors not considered in the theoretical calculations. From this result, it can be concluded that the reductions of the line lengths of Jigs-A and -B, and the Appl. Sci. 2019, 9, 4084 13 of 17 mounting plate as well as the employment of low thermal expansion materials for the Jig-B and jigs in the overall setup, are expected to stabilize the femtosecond laser chromatic confocal probe.

Table 3. Summary of the contribution of each factor on the overall thermal stability of the setup.

Item Factor value Refractive index instability of the chromatic objective lens P = 0.0151 µm/ C 1 − ◦ Refractive index instability of the surrounding air P = 0.0247 µm/ C 2 − ◦ Probe Thermal expansion of mechanical jigs P3 = 4.96 µm/◦C Thermal expansion of optical path length P = 0.0555 µm/ C 4 − ◦ P = P + P + P + P Thermal stability of the probe 1 2 3 4 = 4.86 µm/◦C

(Thermal expansion of a sample) (S1) (Sample unit) (Thermal expansion of sample jig) (S2) (S = S + S ) (Thermal stability of the sample unit) 1 2 Not considered Thermal expansion of the mounting plate, corresponding to the Mounting plate M = 0.735 µm/ C thermal stability of the mounting plate − ◦ O = P + S + M Thermal stability of the overall setup = 4.13 µm/◦C

4. Improvement of the Thermal Stability of the Femtosecond Laser Chromatic Confocal Probe Aiming to improve the thermal stability of the chromatic confocal probe, a second prototype measurement setup was newly designed and developed. It should be noted that the thermal stability of the overall chromatic confocal measurement setup is contributed by not only the thermal stability of the chromatic confocal probe itself but also the thermal stabilities of the sample, the sample jig, and the mounting plate. This paper is focused on the improvement of the thermal stability of the chromatic confocal probe itself, since the thermal stabilities of the sample, the sample jigs, and the mounting plate change when the probe is employed for different applications. To improve the thermal stability of the femtosecond laser chromatic confocal probe, attentions were paid to choose a material having a low thermal expansion coefficient for the major mechanical component (Jig-B) in the chromatic confocal probe, while the optical path length was designed to be as short as possible. Figure 11 compares the previous first prototype measurement setup and the newly developed second prototype measurement setup. As can be seen in the figure, the size of the second prototype measurement setup is reduced to be 1/6 of that of the first prototype measurement setup. For a fair comparison, optical components identical to those employed in the first prototype measurement setup were employed in the second prototype measurement setup, while the material of Jig-B was switched from aluminum to Super Invar having a far lower thermal expansion coefficient compared with aluminum [35,36]. All the optical components and jigs were mounted on an aluminum optical breadboard. At first, the improvement of the thermal stability of the second prototype measurement setup was verified in theoretical calculations. By the modifications described above, the optical path length in the second prototype measurement setup was reduced to be approximately 1/6 of that of the previous first prototype measurement setup. The thermal stability of the newly designed second prototype measurement setup is estimated in the same manner as the previous first prototype measurement setup described in the previous section of this paper. Table4 summarizes the contribution of each factor in the thermal stability of the probe in the second prototype measurement setup. The thermal stability of the chromatic confocal probe in the second prototype measurement setup (0.0197 µm/◦C) is far better than that in the first prototype measurement setup (4.86 µm/◦C). This result implies that the sub-micrometric stability of the femtosecond laser chromatic confocal probe can be achieved by the second prototype measurement setup. Appl. Sci. 2019, 9, 4084 14 of 17 Appl. Sci. 2019, 9, x FOR PEER REVIEW 14 of 18

(a) (b)

FigureFigure 11. 11.Comparison Comparison of of the the size size of theof the previous previous first first prototype prototype measurement measurement setup setup with with that ofthat the of newlythe newly designed designed second second prototype prototype measurement measurement setup: (a setup:) A photograph (a) A photograph of the previous of the first previous prototype first measurementprototype measurement setup; (b) A photograph setup; (b) of A the photograph newly designed of the second newly prototype designed measurement second prototype setup. measurement setup. Table 4. Theoretically estimated thermal stabilities of the previous first prototype probe and the newly designed second prototype probe. At first, the improvement of the thermal stability of the second prototype measurement setup was verified in theoretical calculations. By the modificationsPrevious described First above,The Newly the Designed optical path Factor and Symbol length in the second prototype measurement setup was reducedPrototype to be approximatelySecond Prototype 1/6 of that of theRefractive previous index first instability prototype of themeasurement chromatic objective setup. lensThe (thermalP ) 0.0151 stabilityµm /ofC the newly0.0151 designedµm/ C second 1 − ◦ − ◦ prototypeRefractive measurement index instability setup of the is surroundingestimated in air the (P2 ) same manner0.0247 µ asm/ ◦ theC previous0.0247 firstµm / prototype◦C − − measurementThermal setup expansion described of mechanical in the previous jigs (P3) section of 4.86 thisµ m paper./◦C Table 0.115 4 summarizesµm/◦C the Thermal expansion of optical path length (P ) 0.0555 µm/ C 0.0555 µm/ C contribution of each factor in the thermal 4 stability of− the probe◦ in the− second prototype◦ measurement Thermalsetup. The stability thermal of the stability probe (P )of the chromatic confocal 4.86 µm/ ◦probeC in the 0.0197 secondµm/ ◦prototypeC measurement setup (0.0197 μm/°C) is far better than that in the first prototype measurement setup (4.86Experiments μm/°C). This were result then carried implies out that to verify the the sub-micrometric improvement of stability the thermal of the stability femtosecond of the second laser prototypechromatic chromatic confocal probe confocal can probe be achieved in the sameby the manner second asprototype the first measurement prototype one setup. described in the previous section. Three repetitive experiments were carried out. Figure 12 shows one of the experimental Table 4. Theoretically estimated thermal stabilities of the previous first prototype probe and the results. A mean value of dλ/dT was evaluated to be 7.9 nm/◦C. Therefore, from Equation (7), the thermal stabilitynewly of thedesigned overall second second prototype prototype probe. measurement setup for axial displacement measurement (dZ/dT)Overall was evaluated as (dZ/dT)Overall = (7.9 nmPrevious/◦C) ( 255 nm/nm) = 2.01 µm/◦C. It should · − The Newly− Designed Second be noted that thisFactor result and contains Symbol the contribution of theFirst thermal expansion of the mounting plate. Prototype To evaluate the thermal instability of the probe, the contributionPrototype of the mounting plate is estimated in theory.Refractive Figure 13index shows instability the schematic of the ofchromatic the chromatic confocal−0.0151 lens and the target sample in the second prototype measurement setup. The mounting plate is made of aluminum having−0.0151 a linearμm/°C thermal objective lens (P1) μm/°C expansion coefficient of 23.1 10 6 C 1 [34]. Regarding a length of the mounting plate (175 mm), Refractive index instability× of the− surrounding◦ − −0.0247 from Equation (12), the contribution of the mounting plate is calculated as−0.0247 (dZ/dT) μm/°C = air (P2) μm/°C Mounting plate (23.1 10 6 C 1) (175/2 mm) = 2.02 µm/ C. Considering the result of the above theoretical calculation, Thermal× − ◦ expansion− · of mechanical− jigs◦ (P3) 4.86 μm/°C 0.115 μm/°C the thermal stability of the second prototype chromatic confocal−0.0555 probe is evaluated as follows: Thermal expansion of optical path length (P4) −0.0555 μm/°C μm/°C (dZ/dT) (dZ/dT) (dZ/dT) Thermal stabilityProbe of the≈ probe (P) Overall − 4.86 μm/°CMounting plate 0.0197 μm/°C (16) = ( 2.01 µm/ C) ( 2.02 µm/ C) = 0.01 µm/ C − ◦ − − ◦ ◦ Experiments were then carried out to verify the improvement of the thermal stability of the secondAs can prototype be seen chromatic in the equation, confocal the probe thermal in the stability same ofmanner the second as the prototype first prototype chromatic one confocaldescribed probein the (0.01 previousµm/◦ C)section. was successfully Three repetitive improved experiments compared were with carried that ofout. the Figure first prototype 12 shows chromatic one of the confocalexperimental probe results. (4.86 µ m A/◦ C). mean The value result of obtained dλ/dT was through evaluated the experiments to be 7.9 nm/°C. was also Therefore, close to that from predictedEquation in (7), the the theoretical thermal calculation stability of (0.0197 the overallµm/◦C), second which prototype also demonstrated measurement the improvement setup for axial of thedisplacement thermal stability measurement of the newly (dZ/dT developed)Overall was second evaluated prototype as (dZ/dT chromatic)Overall = confocal(7.9 nm/°C)·(−255 probe. nm/nm) = −2.01 μm/°C. It should be noted that this result contains the contribution of the thermal expansion of the mounting plate. To evaluate the thermal instability of the probe, the contribution of the Appl. Sci. 2019, 9, x FOR PEER REVIEW 15 of 18 Appl. Sci. 2019, 9, x FOR PEER REVIEW 15 of 18 mounting plate is estimated in theory. Figure 13 shows the schematic of the chromatic confocal lens mountingand the target plate sample is estimated in the in second theory. prototype Figure 13 measurement shows the schematic setup. The of themounting chromatic plate confocal is made lens of andaluminum the target having sample a linear in the thermal second expansion prototype coefficient measurement of 23.1 setup. × 10 The−6 °C mounting−1 [34]. Regarding plate is madea length of aluminumof the mounting having platea linear (175 thermal mm), expansion from Equation coefficient (12), theof 23.1 contribution × 10−6 °C −1 of [34]. the Regarding mounting a plate length is ofcalculated the mounting as (dZ /dT plate)Mounting (175 plate mm), = (23.1 from × 10 Equation−6 °C−1)·(175/2 (12), mm) the contribution = −2.02 μm/°C. of theConsidering mounting the plate result is calculatedof the above as theoretical(dZ/dT)Mounting calculation, plate = (23.1 the × thermal10−6 °C−1 stability)·(175/2 mm)of the = second−2.02 μm/°C. prototype Considering chromatic the confocal result ofprobe the aboveis evaluated theoretical as follows: calculation, the thermal stability of the second prototype chromatic confocal probe is evaluated as follows: dZ dT dZ dT  dZ dT  Probe  Overall  Mounting plate dZ dT dZ dT  dZ dT (16)  Probe  Overall  Mounting plate ( 2.01 m m/ C) ( 2.02 m m/ C) 0.01 m m/ C (16) ( 2.01 m m/ C) ( 2.02 m m/ C) 0.01 m m/ C As can be seen in the equation, the thermal stability of the second prototype chromatic confocalAs canprobe be (0.01 seen μm/°C) in the was equation, successfully the thermal improved stability compared of the with second that of prototype the first chromaticprototype confocalchromatic probe confocal (0.01 probe μm/°C) (4.86 was μm/°C). successfully The result improved obtained compared through with the experiments that of the first was prototypealso close chromaticto that predicted confocal inprobe the (4.86 theoretical μm/°C). calculation The result obtained (0.0197 μm/°C),through the which experiments also demonstrated was also close the toimprovement that predicted of the in thermal the theoretical stability of calculation the newly (0.0197developed μm/°C), second which prototype also chromatic demonstrated confocal the improvement of the thermal stability of the newly developed second prototype chromatic confocal Appl.probe. Sci. 2019, 9, 4084 15 of 17 probe. 1575 22.0

1575 Temperature 22.0 ˚C T

Temperature ˚C nm 1570 Wavelength 21.8 T nm 1570 Wavelength 21.8

focused 1565 21.6 

-T Sensitivity : 7.7 nm/˚C Temperature Focused wavelength Focused

1560 -T Sensitivity : 7.7 nm/˚C 21.4 Temperature Focused wavelength Focused 1560 0 1000 2000 3000 4000 500021.4 0 1000 2000Time3000 s 4000 5000 Time s

FigureFigure 12. 12. The thermal stability stability of of focused focused wavelength wavelength λλfocusedfocused of the overall second second prototype prototype measurementFiguremeasurement 12. The setupsetup thermal shownshown stability inin FigureFigure of 1111b. focusedb. wavelength λfocused of the overall second prototype measurement setup shown in Figure 11b.

Figure 13. A schematic of the chromatic confocal lens and the target sample in the second prototype chromaticFigure 13. confocalA schematic measurement of the chromatic setup shown confocal in Figurelens and 11 b.the target sample in the second prototype Figurechromatic 13. confocalA schematic measurement of the chromatic setup shown confocal in lensFigure and 11b. the target sample in the second prototype 5. Conclusionschromatic confocal measurement setup shown in Figure 11b. 5. ConclusionsIn this paper, efforts have been made to improve the thermal stability of the chromatic confocal 5. Conclusions probeIn with this a paper, mode-locked efforts femtosecondhave been made laser to source. improve At the first, thermal the thermal stability characteristics of the chromatic of the previousconfocal firstprobe prototypeIn withthis paper, a femtosecondmode-locked efforts have laser femtosecond been chromatic made to laser confocal improve source. measurement the At thermal first, thestability setup thermal have of the been characteristics chromatic verified confocal through of the experiments,probeprevious with first a and mode-locked prototype the thermal femtosecond femtosecond stability has laser been laser chromaticevaluated source. At to confocal be first, 5.20 the µ measurementm thermal/◦C. Theoretical characteristics setup investigations have of been the onpreviousverified the possible through first prototype reasons experiments, for femtosecond the thermaland the laser instability thermal chromatic stability of the confocal probe, has been such measurement evaluated as the thermal to setup be instability 5.20 have μm/°C. been of theverified refractive through index experiments, of the confocal and lens the and thermal the thermal stability expansion has been of evaluated mechanical to jigs be of 5.20 the μm/°C. probe, have then been carried out. Through the quantitative analysis of the contribution of each possible reason, the mechanical jig, on which the lens holder is mounted, and the mounting plate have been found to be major contributors in the instability of the measurement setup. Regarding the results of theoretical investigations, the second prototype measurement setup has newly been designed and developed. In the second prototype measurement setup, attentions have been paid to minimize the optical path length of the laser beam in the setup, while Super Invar has been employed as the material for the mechanical jig for the improvement of the thermal stability of the chromatic confocal probe. The results of theoretical calculations and experiments have demonstrated that the femtosecond laser chromatic confocal probe in the second prototype measurement setup has achieved thermal stability of 0.01 µm/◦C, which is far better than that in the previous first prototype measurement setup (4.86 µm/◦C). It should be noted that attention has been paid in this paper to improving the thermal stability of the chromatic confocal probe with a mode-locked femtosecond laser source. Application of the developed optical setup for surface profile measurement is the next step of the research, and will be carried out in future work. Appl. Sci. 2019, 9, 4084 16 of 17

Author Contributions: Conceptualization, W.G. and Y.S.; methodology, R.S. and H.M.; software, R.S.; validation, R.S. and H.M.; formal Analysis, R.S., C.C. and Y.S.; investigation, R.S. and C.C.; resources, R.S.; data Curation, R.S. and H.M.; Writing-Original Draft Preparation, R.S. and Y.S.; Writing-Review & Editing, W.G. and Y.S.; Visualization, W.G. and Y.S.; Supervision, W.G.; Project Administration, W.G.; Funding Acquisition, W.G., Y.S. and H.M. Funding: This work is supported by the Japan Society for the Promotion of Science (JSPS). Acknowledgments: The authors would like to thank Taku Nakamura for his help in the preparation of the experimental setup. Conﬂicts of Interest: The authors declare no conﬂicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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