The Improvement on the Performance of DMD Hadamard Transform Near-Infrared Spectrometer by Double Filter Strategy and a New Hadamard Mask

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Article The Improvement on the Performance of DMD Hadamard Transform Near-Infrared Spectrometer by Double Filter Strategy and a New Hadamard Mask

Zifeng Lu 1,2, Jinghang Zhang 1, Hua Liu 1,2,*, Jialin Xu 3 and Jinhuan Li 1,2

1 Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, 5268 Renmin Street, Changchun 130024, China; [email protected] (Z.L.); [email protected] (J.Z.); [email protected] (J.L.) 2 Demonstration Center for Experimental Physics Education, Northeast Normal University, 5268 Renmin Street, Changchun 130024, China 3 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; [email protected] * Correspondence: [email protected]; Tel.: +86-180-0443-0180

Received: 7 December 2018; Accepted: 15 February 2019; Published: 23 February 2019

Abstract: In the Hadamard transform (HT) near-infrared (NIR) spectrometer, there are defects that can create a nonuniform distribution of spectral energy, significantly influencing the absorbance of the whole spectrum, generating stray light, and making the signal-to-noise ratio (SNR) of the spectrum inconsistent. To address this issue and improve the performance of the digital micromirror device (DMD) Hadamard transform near-infrared spectrometer, a split waveband scan mode is proposed to mitigate the impact of the stray light, and a new Hadamard mask of variable-width stripes is put forward to improve the SNR of the spectrometer. The results of the simulations and experiments indicate that by the new scan mode and Hadamard mask, the influence of stray light is restrained and reduced. In addition, the SNR of the spectrometer also is increased.

Keywords: spectrometer; infrared; digital micromirror device (DMD); signal-to-noise ratio (SNR); stray light

1. Introduction In the 1970s, the Hadamard transform (HT) was proposed and developed into a relatively mature theory [1]. With the emergence of the mechanical encoding mask, the HT was applied to the near-infrared (NIR) spectrometer. The encoding mask is a key device in spectrometers. However, adopting the mechanical mask, the spectrometer exhibits a complex structure, low resolution, and short life. Compared with the traditional instrument, it possesses no advantage. The development of HT spectrometers is restricted by the encoding mask. Later, the digital micromirror device (DMD) was developed and applied to the HT spectrometer as an encoding mask. Because the HT spectrometer based on the DMD has several advantages such as a higher signal-to-noise ratio (SNR), wider spectral range, and low cost [2,3], DMD-based HT spectrometers have attracted significant research attention. At present, the performance of HT spectrometers has been greatly improved, but they still have defects, such as the grating diffraction of the spectrometer, the two-dimensional grating diffraction of the DMD, and the poor spectral efficiency of the light source; these defects can make the spectral energy distribution uneven. Thus, the influence of stray light on the absorbance of the whole spectrum is varied; the lower the spectral energy is, the greater the influence by stray light is. The low-energy spectral band exhibits a low SNR, nonlinearity, whereas the high-energy spectral

Micromachines 2019, 10, 149; doi:10.3390/mi10020149 www.mdpi.com/journal/micromachines MicromachinesMicromachines 20182019,, 910, x, 149FOR PEER REVIEW 2 2 of of 13 13 low-energy spectral band exhibits a low SNR, nonlinearity, whereas the high-energy spectral band performsband performs well in wellthose in aspects. those aspects.To improve To improvethe energy the of energythe entire of thespectrum, entire Wang spectrum, and colleagues Wang and proposedcolleagues a proposedspectrum-folded a spectrum-folded structure of a structure HT spectr ofometer a HT and spectrometer a special illumination and a special optical illumination device, butoptical the device,structure but of the the structure spectrometer of the was spectrometer complex [4,5]. was complexZhang et [ 4al.,5 ].proposed Zhang et a al. new proposed algorithm a new to realizealgorithm energy to realize compensation energy compensation of the spectrum of and the spectrumanalyzed andthe effect analyzed of the the HT effect on the of thenoise HT without on the consideringnoise without the considering noise distribution the noise [6]. distribution Quan et [6al.]. Quananalyzed et al. the analyzed spectral the distortion spectral distortion in the HT in spectrometerthe HT spectrometer and presented and presented a correction a correction approach approach [7]. However, [7]. However, for forthe the analysis analysis of of stray stray light, light, especiallyespecially thatthat with with a higha high correlation correlation of energy of distribution,energy distribution, their processing their effectprocessing was unsatisfactory. effect was unsatisfactory.Xu et al. analyzed Xu et the al. influence analyzed of the the influence HT on the of noisethe HT before on the and noise after before coding. and They after also coding. proposed They alsoa new proposed encoding a new mask encoding to correct mask the anomalyto correct inthe the anomaly spectra in caused the spectra by optical caused defects by optical [8]. With defects the [8].variation With the in variation the height inof the the heig stripes,ht of the their stripes, new their encoding new encodi maskng exhibited mask exhibited a low utilization a low utilization rate of ratethe DMD.of the DMD. ToTo improve the performance of the DMD HT NIR spectrometer, a new method of the split waveband scanning is proposed in this paper to mitigate the impact of the stray light. It It can can not not only only reducereduce the influenceinfluence ofof stray stray light light on on the the low-energy low-energy spectral spectral bands, bands, but but also also improve improve the linearitythe linearity and andaccuracy accuracy of absorbance of absorbance in the in low-energy the low-energy spectral spectral bands. bands. On the On other the other hand, hand, a new a Hadamardnew Hadamard mask maskof variable of variable width-stripe width-stripe matching matching with each with scanning each scanning area is area presented is presented to improve to improve SNR.Based SNR. onBased the onnew the scanning new scanning method method and coding and coding mask, the mask, simulation the simulation and experimental and experimental results indicate results thatindicate the straythat thelight stray is suppressed light is suppressed and the spectral and the energy spectral distribution energy distribution is more uniform. is more Theuniform. SNR ofThe the SNR spectrum of the spectrumis also improved, is also especiallyimproved, in especially the low-energy in the spectral low-energy band thespectral SNR isband increased the SNR significantly. is increased It is significantly.demonstrated It thatis demonstrated by the proposed that approach,by the proposed the minimum approach, SNR the in minimum the low-energy SNR in spectralthe low-energy band is spectralimproved band by ais factor improved of 7.434 by a greater factor thanof 7.434 that greater of the traditionalthan that of HT the method. traditional HT method.

2. Theory of Hadamard Transform (HT) Spectrometer with Digital Micromirror Device (DMD) 2. Theory of Hadamard Transform (HT) Spectrometer with Digital Micromirror Device (DMD) AA schematic of the spectrometer designed by us is illustrated in Figure 11a.a. TheThe incidentincident lightlight emittedemitted from thethe samplesample poolpool is is dispersed dispersed by by the the grating, grating, and and the the dispersion dispersion spectrum spectrum imaged imaged on theon theDMD DMD plane plane by theby the imaging imaging lens lens is encoded is encoded and and reflected. reflected. Then, Then, the the reflected reflected light light is focused is focused onto onto the thedetector detector by the by convergingthe converging lens. Finally,lens. Finally, the detector the detector signal issignal decoded is decoded and processed and processed by a computer. by a computer.Because DMD Because is programmable, DMD is programmable, multiple scan multiple modes scan are availablemodes are to available the spectrometer to the spectrometer such as the suchcolumn as the scan column mode, scan the Hadamard mode, the scanHadamard mode, andscan other mode, multiplexed and other scanmultiplexed mode. To scan our mode. spectrometer, To our spectrometer,the major scan the mode major is Hadamardscan mode scan. is Hadamard The coding scan. matrix The of coding the Hadamard matrix spectrometerof the Hadamard is an spectrometerS-matrix determined is an S-matrix by quadratic determined residue by quadrati methodc andresidue can method be used and to describecan be used the to patterns describe to the be patternsdisplayed to onbe thedisplayed DMD [ 9on]. Bythe thisDMD approach, [9]. By this the approach, spectrum canthe bespectrum modified. can be modified.

FigureFigure 1. 1. (a()a )Optical Optical system system of of Hadamard Hadamard transform transform (HT) (HT) spectrometer. spectrometer. (b) (Opticalb) Optical structure structure of HT of spectrometer.HT spectrometer.

Based on our theory, the HT NIR spectrometer with a DMD can be realized. The photograph of the spectrometer is shown in Figure1b. The parameters of the spectrometer are listed in Table1. Before the spectrometer is used, the calibration must be performed to get the relationship between

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Table 1. Parameters of the HT near-infrared (NIR) spectrometer.

Components Micromachines 2019, 10, 149 Model/Parameters Technical Indexes Parameters 3 of 13 Light source Tungsten lamp Spectral range 1350–2450 nm the wavelengthSlit and the pixel 50 location µm in the DMD column. Spectral resolution Three lasers ≤ 8 whose nm wavelengths are respectively 1550Grating nm, 1625 nm, 200 and lines/mm 2210 nm are used DMD to calibrate resolution approximately 912 × 1140 the spectrometer, and a Xenon CalibrationDMD Light DLP4500NIR Source of Ocean Optics Sampling is used rate to perform 1 s the accuracy calibration. The detailed calibration process of the spectrometer can be found in reference [10]. DMD mirrors Aluminum micromirror OpticalTable fibers 1. Parameters Infrared quartz of the HT near-infrared (NIR) spectrometer.

ComponentsDetector InGaAs Model/Parameters R = 3mm Technical Indexes Parameters Light source Tungsten lamp Spectral range 1350–2450 nm BasedSlit on our theory, the50 HTµm NIR spectrometer wi Spectralth a DMD resolution can be realized.≤ 8 nm The photograph of the spectrometerGrating is shown in200 Figure lines/mm 1b. The parame DMDters of resolution the spectrometer 912 × are1140 listed in Table 1. Before theDMD spectrometer is used,DLP4500NIR the calibration must Samplingbe performed rate to get 1 the s relationship between the wavelengthDMD mirrorsand the pixelAluminum location micromirrorin the DMD column. - Three lasers - whose wavelengths are Infrared quartz - - respectivelyOptical 1550 ﬁbersnm, 1625 nm, and 2210 nm are used to calibrate approximately the spectrometer, Detector InGaAs R = 3 mm - - and a Xenon Calibration Light Source of Ocean Optics is used to perform the accuracy calibration. The detailed calibration process of the spectrometer can be found in reference [10]. TheThe spectrumspectrum of the the light light source source tested tested by bythe the spec spectrometertrometer designed designed by us by is uspresented is presented in Figure in Figure2. The2 relative. The relative spectral spectral energy energy is high isin highthe range in the of range 1350–2200 of 1350–2200 nm and nmlow andin the low range in the of 2200–2450 range of 2200–2450nm. The spectral nm. The curves spectral tested curves by some tested other by some spectrometers other spectrometers with different with designs different may designs have maysome havedifferences, some differences, but the spectral but the distribution spectral distribution is the same. is the The same. energy The in energy the central in the wavelength central wavelength band of bandthe spectrum of the spectrum is high isand high those and on those the two on the edges two are edges low. are low.

Figure 2. Light source spectrum. Figure 2. Light source spectrum. 3. The Measurement Result Increase in the Low-Energy Spectral-Band Absorbance 3. The Measurement Result Increase in the Low-Energy Spectral-Band Absorbance 3.1. Impact of Stray Light on the Spectral Band with Different Energies 3.1. Impact of Stray Light on the Spectral Band with Different Energies Stray light is an important measurement parameter of the spectrometers. The existence of the stray light resultsStray light in the is significant an important measurement measurement errors parameter [11]. Especially of the to spectrometers. the dispersive spectrometer,The existence it of may the causestray thelight nonlinear results problems in the ofsignificant the instrument. measurement Thus, it iserrors critical [11]. to suppressEspecially the strayto the light. dispersive In this study,spectrometer, the stray it light may originates cause the mainly nonlinear from problems the scattered of the light instrument. and reflected Thus, light it is of critical the spectrometer. to suppress Whenthe stray the detectorlight. In receivesthis study, a certain the stray wavelength light originates signal, it mainly always from mixes the with scattered some stray light light, and whichreflected is notlight part of ofthe the spectrometer. signal. The existence When the of detector stray light receiv willes reduce a certain the measuredwavelength absorbance, signal, it always especially mixes in spectralwith some bands stray with light, strong which absorption is not part [8]. of the signal. The existence of stray light will reduce the measuredThis type absorbance, of stray especially light is very in spectral complex. bands It maywith leadstrong to absorption a test result [8]. with a homogeneous background. The background values can be measured before beginning the spectral test. When the DMD is closed, the signals received by the detector are the background values. By subtracting the background values from the spectral test signals, the influence of a large proportion of stray light can be corrected. Thus, its performance optimization may be less expensive than other spectrum analysis Micromachines 2019, 10, 149 4 of 13 systems. Beyond that, there is still a fraction of stray light remaining in the energy distribution of the spectrum that cannot be corrected by this method. Using the Zemax software, we can build a nonsequence mode of the optical structure of the spectrometer. By this mode, the energy distribution of the slit images can be obtained in different wavelength bands on the surface of the DMD. The irradiance of the slit image at a wavelength of 1600 nm is shown in Figure3. In this Figure, the energy of the slit image is the highest and there exist other stray lights with a lower energy around the slit image, except for the background light. Because of the secondary reflection of the devices in the spectrometer, there are two energy circles around the slit image, which may be related to the energy distribution of the slit. The secondary reflection mainly comes from the front and rear surfaces of the DMD window. In addition, ghosting can be observed under the slit image, which is formed by the window of the DMD. Because the micromirrors of DMD are easily broken, the optical window is a must to protect them from the surroundings and permit the light of a certain wavelength range to transmit. The material of the DMD window is a kind of optical glass (Corning 7056) whose main constituent is SiO2. For visible, near infrared and ultraviolet wavebands, the anti-reflection films covered on the glasses are different. The refractive index of this type of glass is 1.487 at the wavelength of 545 nm, and the cutoff wavelength for transmission is 2.7 µm. Because the transmission of the DMD window in 1700–2500 nm is reduced, the absorption and reflection are strengthened. So, ghosting can’t be avoided in a carefully designed spectrometer because of the characteristics of DMD. The stray lights formed by the secondary reflection have a great influence on the absorbance measurements of the low-energy spectrumMicromachines [7 2018]. , 9, x FOR PEER REVIEW 4 of 13

Figure 3. Incoherent radiation of slit image.

Therefore,This type of we stray conduct light some is very analyses complex. to determine It may lead the inﬂuence to a test ofresult stray with light. a The homogeneous absorption spectrumbackground. of The 95% background ethanol is values respectively can be measuredmeasured before by our beginni spectrometerng the spectral and UV-Visible/NIR test. When the SpectrophotometerDMD is closed, the UH4150signals received produced by bythe Hitachi detector High are the Technologies background Corporation values. By (Tokyo,subtracting Japan), the asbackground shown in Figurevalues 4from. From the Figure spectral4, wetest can signals, see some the influence stronger of absorption a large proportion peaks of theof stray C–H, light C–H can2, andbe corrected. O–H bending Thus, its and performance harmonic vibrationoptimization in ethanol may be alwaysless expensive exist in than the other long-wavelength spectrum analysis band. However,systems. Beyond some peakthat, there values is arestill less a fraction accurate of stray than light the reference remaining and in the some energy weak distribution peaks cannot of the be observed.spectrum that In 2200–2450 cannot be nm, corrected the three by peaksthis me shownthod. byUsing black the line Zemax B move software, about 1–1.5we can nm build in the a directionnonsequence of long mode wave of the and optical two structure peaks at 2280of the and spectrometer. 2297 nm are By notthis observedmode, the comparedenergy distribution with the blueof the line slit A; images In 1400–2200 can be obtained nm, there in is different also a red wavelength shift of 1.3–3 bands nm on at allthe peaks surface except of the at 1693,DMD. 1760, The andirradiance 1937 nm of the compared slit image with at a the wavelength reference spectrum.of 1600 nmIt ismay shown be in caused Figure by 3. the In this inaccurate Figure, calibrationthe energy of the slit spectrometer image is the and highest the lack and of there the data exist points other stray collected lights by with our a spectrometer. lower energyComparing around the theslit measuredimage, except spectrum for the with background the reference light. spectrum, Because itof showsthe secondary some deviations reflection of of absorption the devices intensity in the betweenspectrometer, the test there values are andtwo theenergy reference circles in around whole wavelengththe slit image, band, which and may the differencebe related ofto absorptionthe energy intensitiesdistribution in of 2200–2450 the slit. The nm secondary is greater than reflection that in mainly 1400–2200 comes nm. from An importantthe front and factor rear is surfaces the stray of light. the WeDMD suppose window that. In when addition, testing ghosting the sample can spectrum,be observed the under low-energy the slit waveband image, which might is be formed disturbed by the by window of the DMD. Because the micromirrors of DMD are easily broken, the optical window is a must to protect them from the surroundings and permit the light of a certain wavelength range to transmit. The material of the DMD window is a kind of optical glass (Corning 7056) whose main constituent is SiO2. For visible, near infrared and ultraviolet wavebands, the anti-reflection films covered on the glasses are different. The refractive index of this type of glass is 1.487 at the wavelength of 545 nm, and the cutoff wavelength for transmission is 2.7 µm. Because the transmission of the DMD window in 1700–2500 nm is reduced, the absorption and reflection are strengthened. So, ghosting can’t be avoided in a carefully designed spectrometer because of the characteristics of DMD. The stray lights formed by the secondary reflection have a great influence on the absorbance measurements of the low-energy spectrum [7].

Micromachines 2019, 10, 149 5 of 13 theMicromachines stray light 2018 from, 9, x the FOR high-energy PEER REVIEW waveband, and the high energy waveband will be affected by 5 the of 13 stray light from the low energy waveband. The inﬂuence of the test results cannot be ignored.

4 B A

Absorbance (AU) 1

0 1400 1600 1800 2000 2200 2400 wavelength(nm)

Figure 4. Absorbance spectrum of 95% ethanol. The blue line A is the reference spectrum tested by the UV-visible/NIRFigure 4. Absorbance spectrophotometer spectrum of UH4150.95% ethanol. The blackThe blue line Bline is theA is absorbance the reference curve spectrum of the tested tested by by thethe traditional UV-visible/NIR scan method. spectrophotometer UH4150. The black line B is the absorbance curve of the tested by the traditional scan method. Then, we perform simulation analysis to verify this hypothesis. The light source is absorbed by the sample.Therefore, The transmission we conduct spectrum some isanalyses received to by determin the detector,e the andinfluence the energy of stray of the light. spectrum The absorption contains twospectrum parts. Oneof is95% from ethanol the transmission is respectively light (Tmeasλ) andured the otherby our is strayspectrometer light (Sλ). and The absorbanceUV-Visible/NIR of a certainSpectrophotometer wavelength of UH4150 the spectrum produced can beby calculatedHitachi Hi bygh theTechnologies following equations:Corporation (Tokyo, Japan), as shown in Figure 4. From Figure 4, we can see some stronger absorption peaks of the C–H, C–H2, and I O–H bending and harmonic vibration inA ethanol= lg alwaλ ys exist, in the long-wavelength band. However, (1) some peak values are less accurate than the referenceTλ + S andλ some weak peaks cannot be observed. In 2200–2450 nm, the three peaks shown by black line B move about 1–1.5 nm in the direction of long Sλ = ∑ kmTλm, (2) wave and two peaks at 2280 and 2297 nm are notm observed compared with the blue line A; In 1400– 2200 nm, there is also a red shift of 1.3–3 nm at all peaks except at 1693, 1760, and 1937 nm compared where I is the spectral intensity at wavelength λ and S denotes the total stray light intensity of the with theλ reference spectrum. It may be caused by the inaccurateλ calibration of the spectrometer and high-energy wavelength band (or low-energy wavelength band). T m is the corresponding intensity the lack of the data points collected by our spectrometer. Comparingλ the measured spectrum with of the sampling points of the transmission light and m is the spectral sampling number. km is the the reference spectrum, it shows some deviations of absorption intensity between the test values and proportion coefficient between the stray light intensity and spectral intensity at a given wavelength. the reference in whole wavelength band, and the difference of absorption intensities in 2200–2450 nm Because each proportion coefficient km is different and complex, we perform simulation experiments is greater than that in 1400–2200 nm. An important factor is the stray light. We suppose that when under the ideal condition, which state that in the same spectral band, the proportion coefficient km of testing the sample spectrum, the low-energy waveband might be disturbed by the stray light from the stray light intensity of each sampling point is replaced by the same coefficient k (k = 0.01, 0.001, the high-energy waveband, and the high energy waveband will be affected by the stray light from 0.0001). To simplify the analysis process, the spectrum is divided into two parts: the high-energy the low energy waveband. The influence of the test results cannot be ignored. wavelength band (1350–2200 nm) and low-energy wavelength band (2200–2450 nm). By this analysis, Then, we perform simulation analysis to verify this hypothesis. The light source is absorbed by we suppose that the stray lights produced by the high-energy wavelength band and low-energy the sample. The transmission spectrum is received by the detector, and the energy of the spectrum wavelength band have different impacts on each other. contains two parts. One is from the transmission light (𝑇 ) and the other is stray light (𝑆 ). The First, we analyze the influence of stray light on the low-energy wavelength band. According to absorbance of a certain wavelength of the spectrum can be calculated by the following equations: the spectrum presented in Figure2, the range of spectral intensity (Iλ) is between 10,000 and 40,000. Assume that the absorbance value of low-energyA=lg wavelengthλ , band is fixed, and set it to be 1. Then the(1) λ intensity of transmission light at a given wavelength: Tλ = 0.1Iλ. In the high-energy wavelength ∑ band, the range of Tλ is between 40,000 and 𝑆 80,000.= 𝑘 By𝑇 solving, Equations (1) and (2), the curve(2) of the intensity effect on the absorbance obtained by the simulation is shown in Figure5. The purple Where 𝐼 is the spectral intensity at wavelength λ and 𝑆 denotes the total stray light intensity of line is the real absorbance. We can see that the lower the transmission light intensity is, the greater the high-energy wavelength band (or low-energy wavelength band). 𝑇 is the corresponding the influence of stray light from the high-energy wavelength band is. The tested values deviate from intensity of the sampling points of the transmission light and m is the spectral sampling number. 𝑘 theis realthe proportion value. Next, coefficient we analyse between the influence the stray of straylight lightintensity on the and high-energy spectral intensity wavelength at a band.given The range of spectral intensities (I ) is between 40,000 and 80,000. Assume that the absorbance value wavelength. Because each proportionλ coefficient 𝑘 is different and complex, we perform ofsimulation high-energy experiments wavelength under band isthe fixed, ideal and condition, set it to bewhich 0.155. state Then that the in intensity the same of transmissionspectral band, light the at a given wavelength: T = 0.7I . In the low-energy wavelength band, the range of T is between proportion coefficient 𝑘λ of theλ stray light intensity of each sampling point is replacedλ by the same coefficient k (k = 0.01, 0.001, 0.0001). To simplify the analysis process, the spectrum is divided into two parts: the high-energy wavelength band (1350–2200 nm) and low-energy wavelength band (2200–

Micromachines 2018, 9, x FOR PEER REVIEW 6 of 13

2450 nm). By this analysis, we suppose that the stray lights produced by the high-energy wavelength band and low-energy wavelength band have different impacts on each other. MicromachinesFirst, we analyze2018, 9, x FOR the PEER influence REVIEW of stray light on the low-energy wavelength band. According 6 of 13 to the spectrum presented in Figure 2, the range of spectral intensity (𝐼) is between 10,000 and 40,000. 2450 nm). By this analysis, we suppose that the stray lights produced by the high-energy wavelength Assume that the absorbance value of low-energy wavelength band is fixed, and set it to be 1. Then band and low-energy wavelength band have different impacts on each other. the intensity of transmission light at a given wavelength: 𝑇 =0.1𝐼. In the high-energy wavelength First, we analyze the influence of stray light on the low-energy wavelength band. According to band, the range of 𝑇 is between 40,000 and 80,000. By solving Equations (1) and (2), the curve of the the spectrum presented in Figure 2, the range of spectral intensity (𝐼) is between 10,000 and 40,000. intensityAssume effect that on the the absorbance absorbance value obtained of low-energy by the wavesimulationlength bandis shown is fixed, in Figure and set 5. it The to be purple 1. Then line is the thereal intensity absorbance. of transmission We can seelight that at a thegiven lower wavelength: the transmission 𝑇 =0.1𝐼. lightIn the intensityhigh-energy is, wavelengththe greater the influenceband, theof strayrange light of 𝑇 from is between the high-energy 40,000 and 80,000. wavele Byngth solving band Equations is. The tested (1) and values (2), the deviate curve of from the the realintensity value. Next, effect weon the analyse absorbance the influence obtained byof thestray simulation light on isthe shown high-energy in Figure 5.wavelength The purple band.line is The rangethe of real spectral absorbance. intensities We can (𝐼 )see is betweenthat the lower 40,000 th eand transmission 80,000. Assume light intensity that the is, absorbance the greater valuethe of high-energyinfluence ofwavelength stray light fromband the is fixed,high-energy and set wavele it to ngthbe 0.155. band Then is. The the tested intensity values of deviate transmission from the light real value. Next, we analyse the influence of stray light on the high-energy wavelength band. The at a given wavelength: 𝑇 =0.7𝐼. In the low-energy wavelength band, the range of 𝑇 is between 𝐼 10,000range and of 40,000. spectral The intensities curve of ( the) is intensitybetween 40,000 that affects and 80,000. the absorbance Assume that obtained the absorbance by the simulation value of is high-energy wavelength band is fixed, and set it to be 0.155. Then the intensity of transmission light shown in Figure 6. From the magnified plot in the inset, the stray light has a small influence on the at a given wavelength: 𝑇 =0.7𝐼. In the low-energy wavelength band, the range of 𝑇 is between high-energy wavelength band. Then, we must address the problem that the low-energy wavelength 10,000 and 40,000. The curve of the intensity that affects the absorbance obtained by the simulation is bandshown with in the Figure strong 6. From absorption the magnified is influenced plot in themo inset,re easily the strayby the light stray has lighta small than influence the high-energy on the wavelength band. high-energyMicromachines wavelength2019, 10, 149 band. Then, we must address the problem that the low-energy wavelength6 of 13 bandThe withsimulation the strong indicates absorption that theis influenced stray light mo hares aeasily great by influence the stray on light the than low-energy the high-energy wavelength band.wavelength In the actual band. measurement, the experimental conditions are more complicated. The intensity of 10,000 and 40,000. The curve of the intensity that affects the absorbance obtained by the simulation is The simulation indicates that the stray light has a great influence on the low-energy wavelength stray lightshown produced in Figure 6by. From each the sampling magnified point plot in has the inset,a different the stray contribution light has a small to influence the transmission on the light intensity.band.high-energy In the actual wavelength measurement, band. Then, the experimental we must address conditions the problem are more that the complicated. low-energy wavelengthThe intensity of strayband light with produced the strong by absorptioneach sampling is influenced point has more a different easily by thecontribution stray light to than the the transmission high-energy light intensity.wavelength band.

Figure 5. Influence of stray light on the low-energy wavelength band. FigureFigure 5. 5.InfluenceInﬂuence of of stray stray light light on thethe low-energy low-energy wavelength wavelength band. band.

Figure 6. Influence of stray light on the high-energy wavelength Band. FigureFigure 6. Influence 6. Inﬂuence of of stray stray light light onon the the high-energy high-energy wavelength wavelength Band. Band.

The simulation indicates that the stray light has a great inﬂuence on the low-energy wavelength band. In the actual measurement, the experimental conditions are more complicated. The intensity of stray light produced by each sampling point has a different contribution to the transmission light intensity.

3.2. Suppression of Stray Light by the Split Waveband Scan Method According to the analysis results, we propose a split waveband scan method. It is similar to the method of decreasing the stray light radiation. We select a filter and place it between the light source and slit. When we choose the high-pass filter, the signals only appear at the short waveband, and at the long waveband, if some signals appear at the same time, it should be the stray light produced by the short waveband. Whereas, if we select the low-pass filter, the result will be reversed. Thus, we canMicromachines obtain the2019 entire, 10, 149 spectrum by combining the parts of two test results which have no 7stray of 13 light. This method can realize the suppression of the stray light. The switching of the filter is realized in front of DMD window by the rotor controlled by the electric system. This method can realize the suppression of the stray light. The switching of the filter is realized in front ofThe DMD absorbance window by curve the rotor of the controlled 95% ethanol by the solution electric system. is shown in Figure 7. As the requirements, our team makeThe absorbancetwo types curveof filters. of the One 95% is ethanol short-wave solution pass is shownfilter whose in Figure cutoff7. As wavelength the requirements, is 2210 nm, andour the team transmission make two typesis higher of filters. than One 95% is in short-wave 1350–2200 pass nm. filter When whose the cutoff wavelength wavelength is greater is 2210 than nm, 2210 nm,and the the transmission transmission will is higher be 0.01%. than The 95% other in 1350–2200 is a long-wave nm. When pass the filter wavelength whose cutoff is greater wavelength than is 21902210 nm, nm, and the the transmission transmission will beis higher 0.01%. Thethan other 95% is in a 2200–2500 long-wave passnm. filterWhen whose the wavelength cutoff wavelength is less than 2190is 2190nm, nm,the transmission and the transmission will be is0.01%.The higher than first 95% filter in 2200–2500 allows high-relative-power nm. When the wavelength waveband is less (1350– 2200than nm) 2190 to pass. nm, the The transmission other one allows will be 0.01%.Thelow relative-power first filter allowswaveband high-relative-power (2200–2450 nm) waveband to pass. When putting(1350–2200 the filters nm) tointo pass. the The spectrometer, other one allows the scan low relative-power waveband has waveband been divided (2200–2450 into two nm) toparts: pass. a high relative-powerWhen putting waveband the filters into and the a low spectrometer, relative-power the scan waveband. waveband At has the been high divided power into waveband, two parts: there a high relative-power waveband and a low relative-power waveband. At the high power waveband, is a noticeable difference between the two curves. This is caused by the decrease of the stray light there is a noticeable difference between the two curves. This is caused by the decrease of the stray light which originates from the low power band. At the low power waveband, the absorbance value tested which originates from the low power band. At the low power waveband, the absorbance value tested by bythe the new new method method is is greater than than that that of theof the traditional traditional method. method. This indicates This indicates that the that method the of method the of thesplit split waveband waveband scan scan can can suppress suppress parts parts of the of the impact impact of the of straythe stray light light and makeand make the measurement the measurement resultresult of ofthe the absorbance absorbance increase. increase.

FigureFigure 7. 7.AbsorbanceAbsorbance spectrum spectrum of 95%95% ethanol. ethanol. The The blue blue line line A isA the is the absorbance absorbance curve curve of the of test the by test by thethe traditional traditional scan scan method. method. The redred line line B B is is the the absorbance absorbance curve curve of the of testthe bytest the by new the scannew method. scan method. 4. SNR Improvement of Low Relative-Power Waveband by a New Hadamard Mask 4. SNR Improvement of Low Relative-Power Waveband by a New Hadamard Mask The NIR analysis technique is based on the small change detection in a strong background signal. TheThe level NIR of analysis the SNR willtechnique have an is impact based on on the the accuracy small change of the analysis detection results, in a whichstrong is background an important signal. Theindicator level of [ 8the]. In SNR part will 3, we have have an already impact provided on the aaccuracy new scan of method the analysis to suppress results, parts which of the strayis an lightimportant indicatorimpact, [8]. but In it can’tpart improve3, we have the SNRalready of the provided low-relative-power a new scan waveband. method to Thus, suppress a new parts Hadamard of the stray lightmask impact, of variable-width but it can’t stripes improve is put forwardthe SNR to addressof the low-relative-power the issue. waveband. Thus, a new Hadamard4.1. Impact mask on SNR of ofvariable-width Different Spectral stripes Energies is put forward to address the issue.

4.1. ImpactThe on noise SNR source of Different of the spectrometer Spectral Energies includes the noise from the detector circuit and light source, which determines the SNR of the HT spectrometer [6,12–15]. Assume that n is the order of Hadamard q The noise source of the spectrometer includes the noise from the detector circuit2n and light source, matrix. The root mean square (RMS) of the illumination noise after the HT will be n+1 times higher which determines the SNR of the HT spectrometer [6,12–15]. Assume that√ n is the order of Hadamard than the original [16]. That of the detector signal noise after the HT will be 2 n times higher than the √ n+1 matrix. The root mean square (RMS) of the illuminationn noise after the HT will be times higher original [15]. Further, the SNR gain becomes 2 [16]. In [8], Xu et al. concluded that if we want to give priority to select the HT scan mode, some conditions should be satisﬁed. When the order n is sufﬁciently large so that the detector noise is equal to the illumination noise, the total noise after the

HT will be lower than that after the column scan. Then, the HT scan mode will be correct. Micromachines 2018, 9, x FOR PEER REVIEW 8 of 13

√ than the original [16]. That of the detector signal noise after the HT will be times higher than the √ original [15]. Further, the SNR gain becomes [16]. In Ref. 8, Xu et al. concluded that if we want to give priority to select the HT scan mode, some conditions should be satisfied. When the order n is sufficiently large so that the detector noise is equal to the illumination noise, the total noise after the HT will be lower than that after the column scan. Then, the HT scan mode will be correct. According to Ref. 8, the SNR for the column scan method and S matrix of the HT is respectively expressed: 𝐷 SNR = (3) (𝐷𝜂) + Δ Micromachines 2019, 10, 149 8 of 13 𝐷 SNR = According to [8], the SNR for the column scan method and S matrix of the HT is respectively expressed: 2𝑛 2√𝑛 (4) (𝐷𝜂 × ) +( Δ) 𝑛+1D 𝑛+1 SNRS = q (3) (Dη)2 + ∆2 Where D is the real spectral intensity of the light source, η is the stability of the light source, Δ is the D electronic system noise collectedSNR by Hthe= analog-to digital converter (AD), and n is the matrix order(4) of r 2 √ 2 q 2n 2 n HT. Based on Equations 3 and 4, we obtainD theη × relationshipn+1 + n +between1 ∆ relative power intensity and SNR, and the relationship between HT order and SNR, as shown in Figures 8 and 9. where D is the real spectral intensity of the light source, η is the stability of the light source, ∆ is the When the order is 107, the RMS of the light source drops off in proportion, and the requirement electronic system noise collected by the analog-to digital converter (AD), and n is the matrix order of of the HT scan mode is satisfied. Figure 8 shows the HT scan has an advantage over the column scan HT. Based on Equations (3) and (4), we obtain the relationship between relative power intensity and methodSNR, under and the the relationship weak light between intensity. HT order and SNR, as shown in Figures8 and9.

FigureFigure 8. Signal-to-noise 8. Signal-to-noise ratio ratio (SNR) (SNR) of oftwo two scan scan meth methodsods for for light light source energyenergy droppingdropping off off in proportion.Micromachinesin proportion. 2018, 9, x FOR PEER REVIEW 9 of 13

FigureFigure 9. 9.SNR SNR of of two two scan scan methods methods for for stable stable light light source. source.

WhenWhen the the order light issource 107, the is stable RMS ofand the n light= 107, source the relative drops offpower in proportion, intensity of and the the spectrum requirement is 10000. of theThe HT curve scan of mode the change is satisﬁed. in SNR Figure following8 shows n is the shown HT scan in Figure has an 9. advantage When the over order the n columnincreases, scan the methodSNR of underthe two the scan weak methods light intensity. tends to be decreased. Whereas, compared with the column scan method,When the the SNR light of source the HT is scan stable method and n = is 107, decrea thesed relative slowly. power Because intensity the light of the source spectrum energy is 10000. has a Thedifferent curve ofdistribution the change in in the SNR entire following waveband,n is shown the SNR in Figure of the9. Whenspectrometer the order willn increases,be influenced. the SNR We ofmust the twothink scan of a methodsmethod to tends change to bethe decreased. condition of Whereas, the nonuniform compared distribution with the column of the spectral scan method, energy and improve the SNR of the spectral edges with low energy.

4.2. Increase in SNR of Low-Energy Waveband by New HT Scan Mask To overcome the impact, we propose a new coding mask, a Hadamard mask of variable-width stripes (VW-Hadamard) in the DMD HT spectrometer. By optimizing the mask, the SNR of the low- energy waveband can be improved. There are three components that determine the resolution: the slit width, the optical transfer function, and DMD resolution. Because of the small pixel size of the DMD, the DMD resolution is not the major determinant [9]. Thus, we plan to change the resolution in different patterns of the DMD. By making sacrifices on the resolution of the edge DMD patterns, the energy loss in the low-energy waveband can be reduced. The width of the scanning stripes is determined by the corresponding spectrum energy in each stripe. The higher the corresponding spectrum energy is, the narrower the stripe width is. Then, the SNR of the edge spectrum with low energy can be improved. Xu et al. proposed a HT scan method by using a mask of variable-height stripes [8]. This method greatly improved the SNR and the even distribution of light source spectral energy. However, because of the change in the height of the stripes, the DMD pattern could not be utilized well. Moreover, a part of the spectral energy was lost. In this study, the VW-Hadamard mask can make full use of the spectral energy because of the adaptive variation in the width of the stripes. The new HT mask has an advantage on the energy utilization over the traditional mask. The flow chart of the mask production is outlined in Figure 10.

Micromachines 2019, 10, 149 9 of 13

the SNR of the HT scan method is decreased slowly. Because the light source energy has a different distribution in the entire waveband, the SNR of the spectrometer will be inﬂuenced. We must think of a method to change the condition of the nonuniform distribution of the spectral energy and improve the SNR of the spectral edges with low energy.

4.2. Increase in SNR of Low-Energy Waveband by New HT Scan Mask To overcome the impact, we propose a new coding mask, a Hadamard mask of variable-width stripes (VW-Hadamard) in the DMD HT spectrometer. By optimizing the mask, the SNR of the low-energy waveband can be improved. There are three components that determine the resolution: the slit width, the optical transfer function, and DMD resolution. Because of the small pixel size of the DMD, the DMD resolution is not the major determinant [9]. Thus, we plan to change the resolution in different patterns of the DMD. By making sacriﬁces on the resolution of the edge DMD patterns, the energy loss in the low-energy waveband can be reduced. The width of the scanning stripes is determined by the corresponding spectrum energy in each stripe. The higher the corresponding spectrum energy is, the narrower the stripe width is. Then, the SNR of the edge spectrum with low energy can be improved. Xu et al. proposed a HT scan method by using a mask of variable-height stripes [8]. This method greatly improved the SNR and the even distribution of light source spectral energy. However, because of the change in the height of the stripes, the DMD pattern could not be utilized well. Moreover, a part of the spectral energy was lost. In this study, the VW-Hadamard mask can make full use of the spectral energy because of the adaptive variation in the width of the stripes. The new HT mask has an advantage on the energy utilization over the traditional mask. The ﬂow Micromachineschart of 2018 the mask, 9, x FOR production PEER REVIEW is outlined in Figure 10. 10 of 13

Figure 10. Figure 10. FlowchartFlowchart of maskmask optimization. optimization.

Assume Em is the median power intensity, and Wm is the strip width of Em, which is taken as the widthAssume of three 𝐸 columnsis the median of the micromirrors. power intensity The width,and 𝑊Wof is the the other strip changing width stripof Em corresponding, which is taken to as the thewidth power of intensitythree columns of E can beof calculated the micromirrors. by The width W of the other changing strip corresponding to the power intensity of E can be calculated by E W m = 𝐸 𝑊 (5) E =Wm (5) 𝐸 𝑊 Whatever the result of the equation is, there exists a maximum wavelength which makes the spectralWhatever waveform the result meaningful. of the equation The spectral is, ther resolutione exists shoulda maximum not go wavelength beyond that. which Figure makes 11a,b the spectralseparately waveform show meaningful. that the traditional The spectral and the newresolu Hadamardtion should mask. not They go beyond are produced that. Figures by the same 11a and 11b orderseparately of 107. show that the traditional and the new Hadamard mask. They are produced by the same order of 107.

Figure 11. Hadamard masks: (a) traditional Hadamard mask (b) new Hadamard mask. They are produced by the same order of 107.

Figure 12. Relative power intensity of the light source. The curves are obtained by the column scan mode with the orders of 107 and 227.

Micromachines 2018, 9, x FOR PEER REVIEW 10 of 13

Figure 10. Flowchart of mask optimization.

Assume 𝐸 is the median power intensity,and 𝑊 is the strip width of Em, which is taken as the width of three columns of the micromirrors. The width W of the other changing strip corresponding to the power intensity of E can be calculated by

𝐸 𝑊 = (5) 𝐸 𝑊 Whatever the result of the equation is, there exists a maximum wavelength which makes the spectral waveform meaningful. The spectral resolution should not go beyond that. Figures 11a and Micromachines11b separately2019 ,show10, 149 that the traditional and the new Hadamard mask. They are produced by10 ofthe 13 same order of 107.

Figure 10. Flowchart of mask optimization.

𝐸 𝑊 = (5) 𝐸 𝑊 Figure 11.11. Hadamard masks: ( a) traditional Hadamard mask ((b)) newnew HadamardHadamard mask.mask. They areare Whateverproduced the result byby thethe same sameof the orderorder equation ofof 107.107. is, there exists a maximum wavelength which makes the spectral waveform meaningful. The spectral resolution should not go beyond that. Figures 11a and In order to verify the performance improvement of the HT spectrometer based on the new coding 11b separately show that the traditional and the new Hadamard mask. They are produced by the mask, we perform some tests on the light source spectrum. The DMD resolution is 912 × 1104. same orderThere of are 107. 912 columns of micromirrors in the direction of the spectrum dispersion. The curves of the relative power intensity acquired by the column scan method with different sampling points are presented in Figure 12. With the increase in the number of sampling points, the spectral energy received by the detector decreases. Furthermore, the distribution of each wavelength corresponding to the energy is more even than before. Considering the curves in Figures9 and 12, the number of sampling points can’t be too large. Thus, we choose the orders of 107 and 227 to perform the test and analysis. The spectrum is divided into two parts: a high-energy wavelength band (1350–2170 nm) and low-energy wavelength band (2170–2450 nm). Based on reference 8, the SNRvi by the new mask scanning method can be calculated by Figure 12. Relative power intensity of the light source. The curves are obtained by the column scan mode with the orders of 107 and 227. Di SNRVi = r (6) q 2 √ 2 (D η × 2Ni ) + ( 2 Ni ∆) i Ni+1 Ni+1

where i denotes the i-th scanning stripe, SNRvi is the SNR of the i-th stripe region, Di is the spectral intensity of the i-th stripe scanning region, and Ni is the matrix order of the HT in the i-th scanning Figurestripe. 11. The Hadamard curves of themasks: spectral (a) SNRtraditional calculated Hadamard by the equations mask (Equations(b) new Hadamard (3), (4) and(6)) mask. are shown They are producedin Figures by the13 and same 14 .order of 107.

Figure 12.Figure Relative 12. Relative power power intensity intensity of ofthe the light light source source.. The The curves curves are are obtained obtained by the by column the column scan scan mode with the orders of 107 and 227. mode with the orders of 107 and 227.

MicromachinesMicromachines 2018 2018, ,9 9, ,x x FOR FOR PEER PEER REVIEW REVIEW 11 11 of of 13 13

InIn orderorder toto verifyverify thethe performanceperformance improvementimprovement ofof thethe HTHT spectrometerspectrometer basedbased onon thethe newnew codingcoding mask, mask, we we perform perform some some tests tests on on the the light light so sourceurce spectrum. spectrum. The The DMD DMD resolution resolution is is 912 912 × × 1104. 1104. ThereThere are are 912 912 columns columns of of micromirrors micromirrors in in the the directio directionn of of the the spectrum spectrum dispersion. dispersion. The The curves curves of of the the relativerelative powerpower intensityintensity acquiredacquired byby thethe columncolumn scanscan methodmethod withwith differentdifferent samplingsampling pointspoints areare presentedpresented inin FigureFigure 12.12. WithWith thethe increaseincrease inin ththee numbernumber ofof samplingsampling points,points, thethe spectralspectral energyenergy receivedreceived by by the the detector detector decreases. decreases. Furthermore, Furthermore, the the distribution distribution of of each each wavelength wavelength corresponding corresponding toto thethe energyenergy isis moremore eveneven thanthan before.before. ConsiderConsideringing thethe curvescurves inin FiguresFigures 99 andand 12,12, thethe numbernumber ofof samplingsampling points points can’t can’t be be too too large. large. Thus, Thus, we we choose choose the the orders orders of of 107 107 and and 227 227 to to perform perform the the test test and and analysis.analysis. TheThe spectrumspectrum isis divideddivided intointo twotwo partparts:s: aa high-energyhigh-energy wavelengthwavelength bandband (1350–2170(1350–2170 nm)nm) and low-energy wavelength band (2170–2450 nm). Based on reference 8, the SNRvi by the new mask and low-energy wavelength band (2170–2450 nm). Based on reference 8, the SNRvi by the new mask scanningscanning method method can can be be calculated calculated by by 𝐷 𝐷 SNR = SNR = 2𝑁 (6) 2𝑁2𝑁 2𝑁 (6) (𝐷𝜂× ) +( Δ) (𝐷𝜂× 𝑁 +1) +(𝑁 +1Δ) 𝑁 +1 𝑁 +1

Where i denotes the i-th scanning stripe, SNRvi is the SNR of the i-th stripe region, Di is the spectral Where i denotes the i-th scanning stripe, SNRvi is the SNR of the i-th stripe region, Di is the spectral intensity of the i-th stripe scanning region, and Ni is the matrix order of the HT in the i-th scanning intensity of the i-th stripe scanning region, and Ni is the matrix order of the HT in the i-th scanning stripe. The curves of the spectral SNR calculated by the equations (Equations 3, 4 and 6) are shown Micromachinesstripe. The curves2019, 10, 149of the spectral SNR calculated by the equations (Equations 3, 4 and 6) are shown11 of 13 inin Figures Figures 13 13 and and 14. 14.

FigureFigure 13. 13. SNR SNR of of the the spectrometer spectrometer with with the the orderorder order ofof of 107.107. 107.

FigureFigure 14. 14. SNR SNR of of the the spectrometer spectrometer with with the the orderorder order ofof of 227.227. 227.

ForForn n= =107, 107, the the average average SNR SNR obtained obtained by by the the V VWW-Hadamard-Hadamard method method ( SNR(SNRV)) inin thethe short-wave short-wave For n = 107, the average SNR obtained by the VW-Hadamard method (SNR) in the short-wave sidebandsideband isis 3289.153,3289.153, whichwhich isis 2.034 2.034 times times that that by by the the scanning scanning spectrometer spectrometer ( SNR(SNRS).). ThatThat byby thethe sideband is 3289.153, which is 2.034 times that by the scanning spectrometer (SNR). That by the traditionaltraditional Hadamard Hadamard method method ( SNR(SNRH)) isis 3293.121,3293.121, whichwhich is is 2.036 2.036 times times that that of ofSNR SNRS.. ForFor the the average average traditional Hadamard method (SNR) is 3293.121, which is 2.036 times that of SNR. For the average SNR in the long-wave sideband (2220–2450 nm), SNRV is 2.972 times that of SNRS and 1.062 times that of SNRH. For the minimum SNR in the short-wave sideband, SNRV is 2.547 times that of SNRS and 1.026 times that of SNRH. For the minimum SNR in the long-wave sideband, SNRV is 11.52 times that of SNRS and 2.213 times that of SNRH. When n = 227, the average SNR of the VW-Hadamard spectrometer is improved compared to that of the Hadamard. Particularly, for the minimum SNR in the long-wave sideband, SNRV is 20.397 times that of SNRS and 2.743 times that of SNRH. According to the results, the VW-Hadamard mask with the order of 227 performs better than that with the order of 107 in the long-wave sideband. The curves of the DMD resolution by the two methods are presented in Figure 15. Because the DMD resolution matches with the spectral resolution, the spectral resolution (the yellow curve) in Figure 15 is the same as the DMD resolution of the traditional Hadamard. From Figure 15, we can see that the DMD resolution has a slight increase in 1450–2220 nm for the new Hadamard when the order is 107 and 227. However, the resolution increase is not useful because the DMD resolution should match with the spectral resolution. This means if the spectral resolution is lower than the DMD resolution, the resolution of the spectrometer will depend on spectral resolution. In 1300–1450 and 2220–2450 nm, the DMD resolution of the new Hadamard is decreased. By combining SNR with the DMD resolution, we conclude the SNR have been improved by means of sacriﬁcing the resolution in the two sideband. Micromachines 2018, 9, x FOR PEER REVIEW 12 of 13

SNR in the long-wave sideband (2220–2450 nm), SNR is 2.972 times that of SNR and 1.062 times that of SNR. For the minimum SNR in the short-wave sideband, SNR is 2.547 times that of SNR and 1.026 times that of SNR. For the minimum SNR in the long-wave sideband, SNR is 11.52 times that of SNR and 2.213 times that of SNR. When n = 227, the average SNR of the VW-Hadamard spectrometer is improved compared to that of the Hadamard. Particularly, for the minimum SNR in the long-wave sideband, SNR is 20.397 times that of SNR and 2.743 times that of SNR. According to the results, the VW-Hadamard mask with the order of 227 performs better than that with the order of 107 inMicromachines the long-wave2019, 10, 149 sideband. 12 of 13

Figure Figure15. Digital 15. Digital micromirror micromirror device device (DMD) (DMD) resolutionresolution of theof the new new Hadamard Hadamard and the and traditional the traditional Hadamard. The blue and red curves are obtained by the V -Hadamard mask. The yellow curve is the Hadamard. The blue and red curves are obtained by theW VW-Hadamard mask. The yellow curve is the spectral resolution which is the same as the DMD resolution of the traditional Hadamard. spectral resolution which is the same as the DMD resolution of the traditional Hadamard. 5. Conclusions The curvesIn HT spectrometersof the DMD with resolution a DMD, weby analyze the two the methods influence of are stray presented light. It is shown in Figure that the 15. stray Because the DMD resolutionlight mainly matches affects the with spectral the energy spectral distribution resolution of the, lightthe source.spectral It canresolution reduce the (the measurement yellow curve) in Figure value15 is ofthe the same spectral as absorbancethe DMD andresolution make the of SNR the inconsistent. traditional We Hadamard. address these From problems Figure from 15, we can see thattwo the aspects. DMD Oneresolution is to mitigate has thea slight impact increase of the stray in light1450–2220 by the double nm for filter the strategy, new Hadamard and the other when the is to improve the SNR by a new Hadamard mask. In addition, the experiments and simulations are order is 107 and 227. However, the resolution increase is not useful because the DMD resolution conducted and compared between the new scanning method and traditional HT scanning method. should Thematch SNRs with of the the spectrometers spectral resolution. are compared This for differentmeans if methods the spectral when the resolution order is 107 is and lower 227. than the DMD resolution,The results demonstratethe resolution that theof the new spectrometer method and mask will can depend effectively on suppressspectralthe resolution. stray light In and 1300–1450 and 2220–2450make the nm, distribution the DMD of the resolution spectral energy of the more new uniform. Hadamard Meanwhile, is decreased. the SNR also By is combining improved. SNR with the DMDAuthor resolution, Contributions: we concludeConceptualization: the SNR H.L. have and J.L.; been methodology: improved J.X.; by software: means J.X.; of validation:sacrificing Z.L., the H.L. resolution in the twoand sideband. J.L.; formal analysis: Z.L.; investigation: J.Z.; resources: H.L.; data curation: J.Z.; writing—original draft preparation: Z.L.; writing—review and editing: Z.L.; visualization: J.L.; supervision: H.L.; project administration: H.L.; funding acquisition: H.L. 5. ConclusionsFunding: The work described in this paper is supported by the National Natural Science Foundation of China under grant No. 61875036, Projects of Science and Technology Development Plan of Jilin Province In (20190302049GX),HT spectrometers the State with Key Laboratorya DMD, of we Applied analyze Optics, the and influence the Lab of Space of stray Optoelectronic light. It Measurement is shown that the stray light& Perception mainly (LabSOMP-2018-05). affects the spectral energy distribution of the light source. It can reduce the Acknowledgments: We acknowledge financial support by the National Natural Science Foundation of measurementChina under value grant of No. the 61875036,spectral Projects absorbance of Science and and make Technology the DevelopmentSNR inconsistent. Plan of Jilin We Province address these problems(20190302049GX), from two theaspects. State Key One Laboratory is to ofmitigate Applied Optics, the andimpact the Lab of of the Space stray Optoelectronic light by Measurement the double filter & Perception (LabSOMP-2018-05). strategy, and the other is to improve the SNR by a new Hadamard mask. In addition, the experiments Conflicts of Interest: The authors declare no conflict of interest. and simulations are conducted and compared between the new scanning method and traditional HT scanningReferences method. 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