DOCSLIB.ORG

Processor U.S

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Processor U.S USOO5926295A United States Patent (19) 11 Patent Number: 5,926,295 Charlot et al. (45) Date of Patent: Jul. 20, 1999 54) HOLOGRAPHIC PROCESS AND DEVICE 4,602,844 7/1986 Sirat et al. ............................. 350/3.83 USING INCOHERENT LIGHT 4,976,504 12/1990 Sirat et al. .. ... 350/3.73 5,011,280 4/1991 Hung.............. ... 356/345 75 Inventors: Didier Charlot, Paris; Yann Malet, 5,081,540 1/1992 Dufresne et al. ... ... 359/30 Saint Cyr l’Ecole, both of France 5,081,541 1/1992 Sirat et al. ...... ... 359/30 5,216,527 6/1993 Sharnoff et al. ... 359/10 73 Assignee: Le Conoscope SA, Paris, France 5,223,966 6/1993 Tomita et al. .......................... 359/108 5,291.314 3/1994 Agranat et al. ......................... 359/100 21 Appl. No.: 08/681,926 22 Filed: Jul. 29, 1996 Primary Examiner Jon W. Henry Attorney, Agent, or Firm Michaelson & Wallace; Peter L. Related U.S. Application Data Michaelson; John C. Pokotylo 62 Division of application No. 08/244.249, filed as application 57 ABSTRACT No. PCT/FR92/01095, Nov. 25, 1992, Pat. No. 5,541,744. An optical device for generating a signal based on a distance 30 Foreign Application Priority Data of an object from the optical device. The optical device includes a first polarizer, a birefringent crystal positioned Nov. 27, 1991 FR France ................................... 91. 14661 optically downstream from the first polarizer, and a Second 51) Int. Cl. .............................. G03H 1/26; G01B 9/021 polarizer arranged optically downstream from the birefrin 52 U.S. Cl. ................................... 359/30; 359/11; 359/1; gent crystal. The Second polarizer creates a pair of inter 359/495; 359/501; 356/345; 356/360 ferograms by adjusting a phase of the light. Two outputs are 58 Field of Search .................................... 359/30, 11, 1, generated by Separately integrating an amount of light of at 359/495, 494, 497, 501; 356/345, 360 least a part of each of the pair of interferograms. Finally, the two outputs are combined Such that the Signal, depending 56) References Cited only on the distance between the object and the optical System, is obtained. U.S. PATENT DOCUMENTS 4,124.278 11/1978 Grinberg et al. ....................... 359/250 38 Claims, 6 Drawing Sheets 32 -1N-N PROCESSOR U.S. Patent Jul. 20, 1999 Sheet 1 of 6 5,926,295 FIG. f. O 32 ? 35 -1N-N 5 -1N 36 12 - S - 33 34 U.S. Patent Jul. 20, 1999 Sheet 2 of 6 5,926,295 FIC, 7 U.S. Patent Jul. 20, 1999 Sheet 3 of 6 5,926,295 DETECTOR 52 FIG. 9 a a w CENTER 5 ||" |/|Y: || 2-1 U.S. Patent Jul. 20, 1999 Sheet 4 of 6 5,926,295 FIC. 1 1 100 130 P v-ap 112 133-1 34 N-N-1 13 132 U.S. Patent Jul. 20, 1999 Sheet S of 6 5,926,295 O N N YN CO N?) n1) N-N-1 N a 3 R S.3-a 2 2 N5 O va s n Nr. 3 U.S. Patent Jul. 20, 1999 Sheet 6 of 6 5,926,295 5,926.295 1 2 HOLOGRAPHIC PROCESS AND DEVICE The interference pattern obtained which represents the USING INCOHERENT LIGHT conoscopic hologram of a point is called Gabor Zone lens. Indeed, the conoscopic hologram of a point recorded at This application is a divisional of our patent application the wavelength ) is similar to the hologram of the same Ser. No. 08/244,249 filed on Oct. 6, 1994 now U.S. Pat. No. point recorded with coherent light (Gabor holography) at an 5,541,744, which was a national Stage of International equivalent wavelength eq given by: Application No. PCT/FR92/01095, filed Nov. 25, 1992. BACKGROUND OF THE INVENTION The present invention describes an improved holographic proceSS and a device using incoherent light. The French Patent Publication No. FR-A-2641091 The principle of incoherent holography and its application describes Some improvements to the System described in to distance measurements have been described in U.S. Pat. U.S. Pat. No. 4,602,844. Still other improvements are No. 4,602,844. This patent describes an optical system described in the French Patent Publication Nos. FR-A- (named “Conoscopic Apparatus) including a birefringent 15 2646251 and FR-A-2646252. uniaxial crystal and two polarizers which permit the holo Until now, to recover the shape of the object, it was gram of a point in incoherent light to be optically formed. proposed to record the holograms on a CCD array or linear If a ray of light impinges on the crystal, the birefringent CCD array, to then digitize the obtained signal, and to properties of the crystal causes the incident light to be split numerically process the digitized signal. The numerical data into two light beams having perpendicular polarizations. process consists mainly of a Fourier transform. The first light beam (ordinary ray) propagates inside the The systems described in the above mentioned documents crystal at a velocity Vo (index of refraction No) independent have a great interest. However, the known Systems which of the propagation direction. The Second light beam include numerical data processing have a limited measure (extraordinary ray) propagates inside the crystal at a Velocity ment time because of the time consumed by the numerical 25 data processing. In addition the quantity of light needed to Ve (index of refraction Ne) which is a function of the achieve a given signal to noise ratio (on which depends the propagation direction. further precision) is proportional to the Square root of the At the first order of approximation on the incidence angle, number of detectors. the two light beams follow the same geometrical path in the The object of present invention is to improve the existing crystal. However, because the two light beams do not devices and to SuppreSS their disadvantages. propagate at the same Velocity, they are out of phase with each other at the exit face of the crystal. SUMMARY OF THE INVENTION The polarizer placed after the crystal will permit the The present invention obtains the above mentioned ordinary and extraordinary vibrations to recombine Such that objects by providing a proceSS including Steps of the phase of the resulting wave is coded in the form of an 35 creating a point hologram by means of an optical device interference Figure. including a crystal and 2 polarizers positioned upstream and The polarizer placed before the crystal permits two rays of downstream the crystal; the same intensity to be obtained Such that a maximum Separately recording the System outputs corresponding to contrast is obtained at the output. two different polarizations, and For a Small incident angle 0, and with a crystal of length 40 L., whose crystallographic optical axis is parallel to the combining these two recordings to give a signal which is optical axis of the System, the phase difference between the function of the distance between the point and the optical ordinary and extraordinary rays induced by passing through System. the crystal is: In a preferred embodiment of the present invention, the 45 combination of the two recordings of the device is based on 1 1 (1) the ratio between a difference and a Sum of the recordings. Acis = *z,ZE 7.)Zo The present invention also concerns a device to imple ment the above described process. BRIEF DESCRIPTION OF THE DRAWINGS where 50 Others characteristics, goals and advantages of the present invention will be clarified in the detailed description of the annexed Figures, given for non limitative examples. The amplitude of the wave in the observation plane is the FIG. 1 is a schematic which represents the structure of a Sum of the ordinary and extraordinary amplitudes. The 55 first device in accordance with present invention. intensity recorded at a point Q (x, y, o) is proportional to: FIGS. 2 to 6 represent interference patterns recorded by a (4a) detector. FIG. 7 represents signal output curves given after pro 60 cessing the Signals recorded by detectors. (4b) FIG. 8 represents a preferential output curve. depending on whether the two polarizers have the same FIG. 9 represents an alternative embodiment of a detec handineSS or not. tion device in accordance with the present invention. In these relationships, I(P) is the intensity of the wave FIG. 10 represents some curves obtained with the detec coming from the object point P(x0,y0,z), onto the detector, 65 tion device of FIG. 9. i.e., this one which should be recorded without the cono FIGS. 11, 12 and 13 represent alternative devices in Scopic part. accordance with the present invention. 5,926.295 3 4 FIG. 14 represents an intensity mask which may be used Moreover, a comparison of the results of the FIGS. 2, 4, in the present invention. and 5 show that, when F increases and Z is fixed, the center FIG. 15 represents a device having autofocus properties in position of the Gabor Zone moves away from the center of accordance with the present invention. the detector 50. The representations given on FIGS. 2 to 6 correspond to DETAILED DESCRIPTION one of the two used polarizations. The interference patterns First Example recorded with the Second polarization are complementary with those illustrated on FIGS. 2 to 6. A first example of the present invention is described referring to FIG. 1. General Information About Processing The optical axis of device 10 is referenced as 12. The device 10 contains: FIG. 7 represents the relationship of the ratio between the a conoscopic System 30 including: difference and sum of the values (S) successively obtained a birefringent crystal 31, and by photodetector 50 by the valve action 38 based on the 15 distance Z for respective F values of 0, 1, 2, 3, 4.
Load more

Recommended publications
  • Lab 8: Polarization of Light
    Lab 8: Polarization of Light 1 Introduction Refer to Appendix D for photos of the appara- tus Polarization is a fundamental property of light and a very important concept of physical optics. Not all sources of light are polarized; for instance, light from an ordinary light bulb is not polarized. In addition to unpolarized light, there is partially polarized light and totally polarized light. Light from a rainbow, reflected sunlight, and coherent laser light are examples of po- larized light. There are three di®erent types of po- larization states: linear, circular and elliptical. Each of these commonly encountered states is characterized Figure 1: (a)Oscillation of E vector, (b)An electromagnetic by a di®ering motion of the electric ¯eld vector with ¯eld. respect to the direction of propagation of the light wave. It is useful to be able to di®erentiate between 2 Background the di®erent types of polarization. Some common de- vices for measuring polarization are linear polarizers and retarders. Polaroid sunglasses are examples of po- Light is a transverse electromagnetic wave. Its prop- larizers. They block certain radiations such as glare agation can therefore be explained by recalling the from reflected sunlight. Polarizers are useful in ob- properties of transverse waves. Picture a transverse taining and analyzing linear polarization. Retarders wave as traced by a point that oscillates sinusoidally (also called wave plates) can alter the type of polar- in a plane, such that the direction of oscillation is ization and/or rotate its direction. They are used in perpendicular to the direction of propagation of the controlling and analyzing polarization states.
    [Show full text]
  • Principles of Retarders
    Polarizers PRINCIPLES OF RETARDERS etarders are used in applications where control or Ranalysis of polarization states is required. Our retarder products include innovative polymer and liquid crystal materials. Crystalline materials such as quartz and Retarders magnesium fluoride are also available upon request. Please call for a custom quote. A retarder (or waveplate) is an optical device that resolves a light wave into two orthogonal linear polarization components and produces a phase shift between them. The resulting light wave is generally of a different polarization form. Ideally, retarders do not polarize, nor do they induce an intensity change in the Crystals Liquid light beam, they simply change its polarization form. state. The transmitted light leaves the retarder elliptically All standard catalog Meadowlark Optics’ retarders are polarized. made from birefringent, uniaxial materials having two Retardance (in waves) is given by: different refractive indices – the extraordinary index ne = ␤tր␭ and the ordinary index no. Light traveling through a retarder has a velocity v where: dependent upon its polarization direction given by ␤ = birefringence (ne - no) Spatial Light ␭ Modulators v = c/n = wavelength of incident light (in nanometers) t = thickness of birefringent element where c is the speed of light in a vacuum and n is the (in nanometers) refractive index parallel to that polarization direction. Retardance can also be expressed in units of length, the By definition, ne > no for a positive uniaxial material. distance that one polarization component is delayed For a positive uniaxial material, the extraordinary axis relative to the other. Retardance is then represented by: is referred to as the slow axis, while the ordinary axis is ␦Ј ␦␭ ␤ referred to as the fast axis.
    [Show full text]
  • Optical and Thin Film Physics Polarisation of Light
    OPTICAL AND THIN FILM PHYSICS POLARISATION OF LIGHT An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular to each other; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels. The rotation can have two possible directions; if the fields rotate in a right hand sense with respect to the direction of wave travel, it is called right circular polarization, while if the fields rotate in a left hand sense, it is called left circular polarization. On the other side of the plate, examine the wave at a point where the fast-polarized component is at maximum. At this point, the slow-polarized component will be passing through zero, since it has been retarded by a quarter-wave or 90° in phase. Moving an eighth wavelength farther, we will note that the two are the same magnitude, but the fast component is decreasing and the slow component is increasing. Moving another eighth wave, we find the slow component is at maximum and the fast component is zero. If the tip of the total electric vector is traced, we find it traces out a helix, with a period of just one wavelength. This describes circularly polarized light. Left-hand polarized light is produced by rotating either the waveplate or the plane of polarization of the incident light 90° .
    [Show full text]
  • Stokes Polarimetry
    photoelastic modulators Stokes Polarimetry APPLICATION NOTE by Dr. Theodore C. Oakberg beforehand. The polarimeter should be aligned so that the James Kemp’s version of the photoelastic modulator was passing axis of the modulator is at 45 degrees to the known invented for use as a polarimeter, particularly for use in linear polarization direction, as shown. The polarizer is oriented astronomy. The basic problem is measuring net polarization at right angles to the plane of the incident linear polarization components in what is predominantly an unpolarized light component. source. Dr. Kemp was able to measure a polarization The circular polarization component will produce a signal at the component of light less than 106 below the level of the total modulator frequency, 1f. If the sense of the circular polarization light intensity. is reversed, this will be shown by an output of opposite sign The polarization state of a light source is represented by four from the lock-in amplifi er. This signal is proportional to Stokes numerical quantities called the “Stokes parameters”.1,2 These Parameter V. correspond to intensities of the light beam after it has passed The linear polarization component will give a signal at twice the through certain devices such as polarized prisms or fi lms and modulator frequency, 2f. A linearly polarized component at right wave plates. These are defi ned in Figure 1. angles to the direction shown will produce a lock-in output with I - total intensity of light beam opposite sign. This signal is proportional to Stokes Parameter U. y DETECTOR y A linear component of polarization which is at 45 degrees to the I x x I x x direction shown will produce no 2f signal in the lock-in amplifi er.
    [Show full text]
  • A Birefringent Polarization Modulator: Application to Phase Measurement in Conoscopic Interference Patterns F
    A birefringent polarization modulator: Application to phase measurement in conoscopic interference patterns F. E. Veiras, M. T. Garea, and L. I. Perez Citation: Review of Scientific Instruments 87, 043113 (2016); doi: 10.1063/1.4947134 View online: http://dx.doi.org/10.1063/1.4947134 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/87/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enhanced performance of semiconductor optical amplifier at high direct modulation speed with birefringent fiber loop AIP Advances 4, 077107 (2014); 10.1063/1.4889869 Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms Rev. Sci. Instrum. 82, 061101 (2011); 10.1063/1.3603452 Birefringence measurement in polarization-sensitive optical coherence tomography using differential- envelope detection method Rev. Sci. Instrum. 81, 053705 (2010); 10.1063/1.3418834 Phase Measurement and Interferometry in Fibre Optic Sensor Systems AIP Conf. Proc. 1236, 24 (2010); 10.1063/1.3426122 Note: Optical Rheometry Using a Rotary Polarization Modulator J. Rheol. 33, 761 (1989); 10.1122/1.550064 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 201.235.243.70 On: Wed, 27 Apr 2016 20:53:51 REVIEW OF SCIENTIFIC INSTRUMENTS 87, 043113 (2016) A birefringent polarization modulator: Application to phase measurement in conoscopic interference patterns F. E. Veiras,1,2,a) M. T. Garea,1 and L. I. Perez1,3 1GLOmAe, Departamento de Física, Facultad de Ingeniería, Universidad de Buenos Aires, Av. Paseo Colón 850, Ciudad Autónoma de Buenos Aires C1063ACV, Argentina 2CONICET, Av.
    [Show full text]
  • Lab #6 Polarization
    EELE482 Fall 2014 Lab #6 Lab #6 Polarization Contents: Pre-laboratory exercise 2 Introduction 2 1. Polarization of the HeNe laser 3 2. Polarizer extinction ratio 4 3. Wave Plates 4 4. Pseudo Isolator 5 References 5 Polarization Page 1 EELE482 Fall 2014 Lab #6 Pre-Laboratory Exercise Bring a pair of polarized sunglasses or other polarized optics to measure in the lab. Introduction The purpose of this lab it to gain familiarity with the concept of polarization, and with various polarization components including glass-film polarizers, polarizing beam splitters, and quarter wave and half wave plates. We will also investigate how reflections can change the polarization state of light. Within the paraxial limit, light propagates as an electromagnetic wave with transverse electric and magnetic (TEM) field directions, where the electric field component is orthogonal to the magnetic field component, and to the direction of propagation. We can account for this vector (directional) nature of the light wave without abandoning our scalar wave treatment if we assume that the x^ -directed electric field component and y^ -directed electric field component are independent of each other. This assumption is valid within the paraxial approximation for isotropic linear media. The “polarization” state of the light wave describes the relationship between these x^ -directed and y^ -directed components of the wave. If the light wave is monochromatic, the x and y components must have a fixed phase relationship to each other. If the tip of the electric field vector E = Ex x^ + Ey y^ were observed over time at a particular z plane, one would see that it traces out an ellipse.
    [Show full text]
  • Polarization Optics
    POLARIZATION OPTICS Retardation Plate Theory Multiple Order Waveplates Achromatic Waveplates A retardation plate is an optically transparent material which As linear polarization enters a crystal, both polarization compo- Using the previous equation, and given a required The wavelength dependence of the birefringence dictates that resolves a beam of polarized light into two orthogonal nents are oscillating in phase with one another. As they propa- retardance value, the necessary thickness of the waveplate the spectral range for the standard waveplate is approximately components; retards the phase of one component relative to gate they begin to fall out of phase due to the velocity differ- can be calculated. For standard waveplate materials, such 10 nm. To accommodate tunable sources or sources with larger the other; then recombines the components into a single ence. Upon exiting, the resultant polarization is some form of as quartz and magnesium fluoride, the calculated thickness spectral widths, a waveplate that is relatively independent of beam with new polarization characteristics. elliptical polarization due to the phase difference. Special polar- for a retardation value of a fraction of a wave would be on wavelength is required This is accomplished with achromatic ization cases can result if the overall phase difference is in multi- the order of 0.1 mm and too thin to manufacture. For this waveplates. ples of � (linear polarization) or �/2 (circular). reason a higher multiple of the required retardation is use to Birefringence place the thickness of the waveplate in a physically manu- An achromatic waveplate is a zero-order waveplate utilizing To better understand phase retardation, birefringence must facturable range.
    [Show full text]
  • Lecture 7: Polarization Elements That We Use in the Lab. Waveplates, Rotators, Faraday Isolators, Beam Displacers, Polarizers, Spatial Light Modulators
    Lecture 7: Polarization elements that we use in the lab. Waveplates, rotators, Faraday isolators, beam displacers, polarizers, spatial light modulators. Polarization elements are important tools for various experiments, starting from interferometry and up to quantum key distribution. This lecture is focused on the commercial polarization elements that one can buy from companies like Thorlabs, Edmund Optics, Laser Components etc. We will consider waveplates and rotators, for polarization transformations, beam displacers and polarization prisms, for the measurement of polarization states, and finally spatial light modulators, elements that use polarization for preparing structured light. 1. Waveplates. A waveplate (retardation plate) can be most simply made out of a piece of crystalline quartz, cut so that the optic axis (z) is in its plane. Quartz is a positive uniaxial crystal, ne no . Therefore, for light polarized linearly along the z-axis, the refractive index n ne , and the phase (and group) velocity is smaller than for light polarized orthogonally to z-axis ( n no ). One says that the z-axis is then ‘the slow axis’, and the other axis is ‘the fast axis’. The fast axis is sometimes marked by a flat cut (Fig.1). A multi-order plate. However, a plate of reasonable thickness (0.5 mm or thicker) will work only for a narrow bandwidth. Indeed, although at Fig.1 the last 2 lectures we assumed that the refractive index is wavelength- independent, in reality it depends on the wavelength. Moreover, even without dispersion the phase would be different for different wavelengths. For instance, at 600 nm, the birefringence is n 0.0091 , and at 700 nm, n 0.0090, nearly the same over 100 nm.
    [Show full text]
  • Waveplate Analyzer Using Binary Magneto-Optic Rotators
    Waveplate analyzer using binary magneto-optic rotators Xiaojun Chen1, Lianshan Yan1, and X. Steve Yao1, 2 1. General Photonics Corp. Chino, CA, 91710, USA Tel: 909-590-5473 Fax: 909-902-5535 2. Polarization Research Center and Key Laboratory of Opto-electronics Information and Technical Science (Ministry of Education), Tianjin University, Tianjin 300072, China *Corresponding Author: [email protected] Abstract: We demonstrate a simple waveplate analyzer to characterize linear retarders using magneto-optic (MO) polarization rotators. The all- solid state device can provide highly accurate measurements for both the retardation of the waveplate and the orientation of optical axes simultaneously. ©2007 Optical Society of America OCIS codes: (120.5410) Polarimetry; (080.2730) Geometrical optics, matrix methods; (060.2300) Fiber measurements; (260.5430) Polarization References and links 1. D. Goldstein, “Polarized light,” (Second Edition, Marcel Dekker, Inc., NY, 2003). 2. E. Collett, Polarized light: Fundamentals and Applications, (Marcel Dekker, New York, 1993) pp. 100-103. 3. H. G. Jerrard, “Optical compensators for measurement of elliptical polarization,” J. Opt. Soc. Am. 38, 35-59 (1948). 4. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676-6683 (1992). 5. E. Dijkstra, H. Meekes, and M. Kremers, “The high-accuracy universal polarimeter,” J. Phys. D 24, 1861- 1868 (1991). 6. P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466-6472 (1997). 7. D. B. Chenault and R. A. Chipman, “Measurements of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter,” Appl. Opt. 32, 3513-3519 (1993).
    [Show full text]
  • Fiber Optic Variable Waveplate
    All-Fiber Variable Waveplate FEATURES: APPLICATIONS: All-fiber Polarization control Simple current control State of polarization scanning Full cycle of Poincare sphere Component testing Low insertion loss Sensor systems High return loss Optical fiber polarimetry Phoenix Photonics variable waveplate is a compact, simple to operate, all-fiber device for wideband operation. Applying a current to the pins gives a controlled modification of the linear birefringence within the device. The input State of polarization can be changed through a full cycle of the Poincare sphere. Two options are available giving flexibility for different applications. Option 1 Single mode (SM) fiber input and output: This version provides a complete cycle of the Poincare sphere to be achieved the range of polarization states generated in the output fiber is dependent on the input SOP. waveplate SM fiber SM fiber Option 2 Polarization maintaining (PM) fiber input and output: This option includes an integrated fiber polarizer in front of the waveplate aligned to the slow axis of the input fiber. The role of the polarizer is to ‘clean’ the linear input state. The output is a PM fiber, in this case the output polarization state will give a full cycle of the great circle on the Poincare sphere. The output from the fiber can be varied through right and left circular and two orthogonal linear states. input polarizer waveplate output PM fiber PM fiber SPECIFICATION: Units Option 1 Option 2 Wavelength range1 nm 1300 - 1610 Insertion Loss2 dB <0.3 <1 PMD ps <0.05 - Return Loss dB >70 Maximum current mA 70 Maximum Voltage V 10 Operating Temperature Range 0C -5 to 70 Storage Temperature 0C -40 to +85 Fiber type SMF28 PANDA Input & Output Fiber Lengths mm 1000 Notes: 1.
    [Show full text]
  • Waveplates Intro Windows
    Waveplates Intro Windows � � Technical Notes . 222 Selection Guide . 225 � Prisms Multiple Order. 226 θ � �� Zero Order Lenses Crystal Quartz . 228 Mica . 230 Mirrors Polymer. 231 Beamsplitters First Order . 232 Dual Wavelength . 233 Waveplates Achromatic Air-Spaced. 234 Polarizers Polymer . 236 Polarization Rotators . 237 Components Ultrafast Etalons Filters Interferometer Accessories ���� ��������������������� Mounts Appendix ������� ���������� Index �������������� Waveplates Intro Technical Notes Waveplates operate by imparting unequal The slow and fast axis phase shifts are � � Windows phase shifts to orthogonally polarized field given by: components of an incident wave. This φs ω ω π λ λ = ns ( ) t/c = 2 ns ( )t/ � causes the conversion of one polarization φf = nf (ω)ωt/c = 2πnf (λ)t/λ Prisms state into another. where ns and nf are, respectively, the θ � indices of refraction along the slow and There are two cases: �� fast axes, and t is the thickness of the Lenses With linear birefringence, the index of waveplate. refraction and hence phase shift differs for two orthogonally polarized linear To further analyze the effect of a waveplate, polarization states. This is the operation we throw away a phase factor lost in Mirrors Figure 1. Orientation of the slow and fast axes measuring intensity, and assign the entire mode of standard waveplates. of a waveplate with respect to an X-polarized phase delay to the slow axis: input field. With circular birefringence, the index of iφ refraction and hence phase shift differs E2 = s(s · E1)e + f(f · E1) For a half waveplate: Beamsplitters φ = φ - φ = 2π(n (λ) - n (λ))t/λ 2 for left and right circularly polarized s f s f φ = (2m + 1)π, T|| = cos 2θ, and = 2π∆n(λ)t/λ 2 components.
    [Show full text]
  • Sources of Error in Retarders and Waveplates
    Sources of Error in Retarders and Waveplates © 2005 Meadowlark Optics, Inc Error sources that afflict true zero order, compound zero order and multi-order linear retarders include variations in temperature, angle of incidence, wavelength, and the presence of multiple reflections. This application note contains technical information designed to aid the user in producing the highest quality results and in making the best purchasing choice among retarder types for the intended application. About linear retarders A retarder, also known as a waveplate, is an optical device that modifies the polarization state of light by resolving it into two orthogonal linear polarization components and producing a phase shift between them. The phase shift results from the two polarization components having different velocities within the retarder material. Generally, waveplates are made from an uniaxial material which is one characterized by a single optic axis and two indices of refraction. The index of refraction along the optic axis is termed the extraordinary index, ne, while that in the plane perpendicular to the optic axis is called the ordinary index, no. The velocity of a component polarized along the optic axis, ve, and one polarized perpendicular to it, vο, is: ve = c/ne and vo= c/no, (1) where c is the speed of light in vacuum. By definition, a positive uniaxial material has a birefringence (ß = ne-no) greater than zero. The slow axis is, therefore, along the optic axis for a positive uniaxial material while the fast axis is along it for a negative uniaxial material. A retarder is typically made by placing the optic axis in the plane of the optic.
    [Show full text]