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Single-exposure polarization phase-shifting interferometer using an azo-polymer orientation array
Optics and Lasers in Engineering 73 (2015) 75–79
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Single-exposure polarization phase-shifting interferometer using an azo-polymer orientation array Peizheng Yan a, Keyi Wang a, Pengcheng Cui a, Jiangang Gao b,n, Jiajun Ma c, Qijin Zhang c a
Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, Anhui, PR China School of Biological and Chemical Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui, PR China c Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei 230026, Anhui, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 5 December 2014 Received in revised form 25 March 2015 Accepted 17 April 2015
We propose a single-exposure polarization phase-shifting interferometer based on a beam-splitting method using an azo-polymer orientation array, which is prepared from an ordinary azo-polymer film with photo-induced optical anisotropy. The azo-polymer orientation array gives a four-step phase shift on the interferogram, from which phase differences between the orthogonal polarized reference and object beam can be calculated. Experimental results are provided to verify the feasibility of the proposed interferometer. The azo-polymer orientation array is easy to fabricate, making this method convenient and low-cost. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Azo-polymer film Photo-induced optical anisotropy Phase-shifting interferometer
1. Introduction Phase-shifting interferometry is an established method for measuring a variety of physical parameters ranging from the surface figure of mirrors to the displacement of solid objects [1]. It has become ubiquitous for the measurement and characterization of many types of surfaces including lenses, mirrors, and aspheres, with various techniques available for analyzing interference data [2,3]. Phase shifting of a wavefront can be accomplished by sequentially introducing a phase step (temporal phase shifting). The largest limitation of temporal phase shifting interferometry for optical testing is the sensitivity to the environment, both vibration and air turbulence. Vibration effects can be reduced by taking all the phase shifted frames simultaneously, which is also called spatial phase shifting. If the interferometer is insensitive to vibration, many measurements can be averaged to reduce the effects of air turbulence. A variety of methods for spatial phase shifting have been developed over the years. The most common ones are the use of multiple cameras to detect multiple interferograms [4], the use of diffractive elements to simultaneously image three or more images onto a single CCD [5] and the use of a tilted reference wave to introduce a spatial carrier frequency into the pattern [6]. The approach with multiple cameras tends to be expensive and difficult to implement. The diffraction approach relies on the diffractive elements, which are expensive and difficult to manufacture. The third method must utilize high precision optics to avoid introducing aberrations between the two non-common path beams.
n
Corresponding author. E-mail address: [email protected] (J. Gao).
http://dx.doi.org/10.1016/j.optlaseng.2015.04.011 0143-8166/& 2015 Elsevier Ltd. All rights reserved.
A far more robust and compact spatial phase-shifting method has been developed by Millerd et al. [7–9], in which a periodic phase-mask array of micro-polarizers is physically attached to a CCD sensor to obtain a unique phase-shift over each pixel. The micropolarizer arrays utilize Moxtek’s wiregrid polarizer technology, which utilizes nanoscale patterning to form a metal grating with sub-wavelength spacing on a thin transparent glass substrate [10]. The wiregrid micro-polarizer array is produced in a multistep lithographic process, which is complex and high-cost. In this paper, we propose a single-exposure phase-shifting interferometer using an azo-polymer orientation array, which is easier to fabricate and low-cost. The azo-polymer orientation array acts as a microretarder array by which different phase shifts are achieved at the pixel-by-pixel level on the interferogram [11]. Azobenzene and its derivatives are excellent photoresponsive materials that can be applied in many domains, including polarization filters, optical data storage, holography, photo-switching of optical elements and lithography [12–21]. The applications of azocontaining materials are based on the photoisomerization action of azochromophores [22] and photo-induced orientation is a remarkable property of azobenzene. Upon illumination with a linearly polarized light at wavelengths below the absorption edge, these azobenzene polymers undergo cycles of cis–trans isomerizations. Every time an azo chromophore undergoes a trans to cis to trans isomerization cycle, its position will vary slightly and randomly, which drive the molecules to align with their major axis perpendicularly to the polarization axis of the incident light [18,23,24]. A high polarizability along the long molecular axis of the azobenzene fragments in the trans conformation determines birefringence effects for the light outside the absorption band [25–27]. The refractive
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P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
index (ne) for the light polarized along the long molecular axis is bigger than the refractive indices (no) in all directions perpendicular to the long molecular axis. Thus, if the polarization orientation of the writing light beam is controlled and can be changed in a well-defined way, it is possible to control the orientation of the birefringence in the polymer and generate space variant retarders. A remarkable aspect of the photoalignment process is that it saturates after enough illumination. If the beam intensity and the exposure time are chosen in a way that the polymer is exposed beyond the saturation, the birefringence is not further increased, which makes the azo-polymer orientation array easy to fabricate. Illumination above the absorption edge of the material does not affect the birefringence and it remains stable [13,28], allowing one to apply the birefringent polymer layer for polarization control.
2. Fabrication of azo-polymer orientation array The azo-polymer (abbreviated as PCN6) used in this part of the work is a conventional side-chain liquid crystalline polymethacrylate bearing azobenzene groups according to previous reports [29,30], of which the wavelength of optical absorption edge is ca. 550 nm. The chemical structure of PCN6 is shown in Fig. 1. A smooth PCN6 film was made by spin-coating with cyclopentanone as a solvent on a 2 cm 2 cm quartz substrate and dried under vacuum at room temperature for 3 days, then the thickness of the transparent film was measured on a Shimadzu UV-2550 UV–vis spectrophotometer to be about 2 μm. The experimental setup used to encode the birefringence in the photopolymer is depicted in Fig. 2. The laser beam at 405 nm is polarized parallel to the y-axis. Azimuth of laser polarization direction through the polarizer, the fast axis of electro-optic modulator and quarter-wave plate with respect to the y-axis are 0, π/4 and 0, respectively. The azo polymer film is mounted on a precision x–ymoving stage and located in the conjugate image plane of the photo mask. The projecting lens has a large aperture (F1.2) and a high resolution (150 lp/mm) and the square photomask and azo film are placed in the center of the lens filed to reduce the impact of diffraction. The photo mask uses a thin film of chrome as an opaque material, which is sputtering coated on Soda Lime glass. On the photo mask shown in Fig. 2, the black area is coated with chrome stopping the laser at 405 nm passing through the photo mask, while chrome in the white area is inductively coupled plasmas etched, with a transmittance value of 88% at 375–450 nm. The period of the photo mask, represented by ‘T’ in Fig. 2, is 50 μm. The magnification of the projection optical system is 0.4 , which means the actual period of the fabricated mask is 20 μm. Four exposures are needed to fabricate of the azo-polymer orientation array. First, set the polarization of the laser beam to π/ 3 by changing the voltage applied to the electro-optic modulator and illuminate the azo polymer for enough time untill it saturates. The exposure area is the projected image of the transparent area on photo mask. Second, move the azo polymer film along the xaxis by T/2, change the polarization of the laser beam to π/6, and illuminate the azo polymer film for enough time. In the third and fourth exposure, move the azo polymer film along the y-axis or xaxis by T/2, change the polarization of the laser beam to π/6 or
Fig. 2. Experimental setup for fabricating the azo-polymer orientation array.
π/3, and illuminate the azo polymer film for enough time again, which is similar to the second step. Because of photo-induced orientation of azobenzene groups, the fast axis of the azo-polymer is the same with the polarization of the laser controlled by the electro-optic modulator. The fast axis of the azo-polymer film after each exposure is shown in Fig. 3. The voltages applied to the electro-optic modulator to set the polarization of the laser beam to the four angles have been calibrated accurately to ensure the spatial variation of the azimuth angle of the optic axis. Only the central 3 mm 3 mm of the whole smooth PCN6 film is used to fabricate the azo-polymer mask, which ensures the uniformity of the film thickness of azo-polymer mask. When the azo polymer is illuminated for enough time until it is saturated, the phase retardation between its fast axis and slow axis reaches a special stable value, which depends on the thickness and chemical component of the film. Therefore, all exposed azo films have the same degree of retardation, which was measured to be 120 degree with the same azo film and laser in our previous work [31]. After four exposures, the azo-polymer is orientated periodically, forming an azo-polymer orientation array. A set of four (2 2) microretarders with the same retardation, whose fast axes have four different angles, are arranged into a “unit cell”, which is repeated continuously over the entire array. Fig. 4 illustrates a unit cell comprised of four microretarders. The retardation uniformity of the azo-polymer orientation array is measured by the polarizing optical microscopy (POM). When the azo-polymer orientation array is rotated to a certain angle, an image is captured by the POM, partly shown in Fig. 5. The line profiles of the retardation in the central row and the central column marked by the red line are also shown in Fig. 5. Although the borders between sub-pixels are blurred because of the diffraction, the retardation uniformity of the azo-polymer orientation array has a good quality of retardation uniformity.
3. Polarization phase-shifting interferometer using an azo-polymer orientation array
Fig. 1. Chemical structure of PCN6.
Using the fabricated azo-polymer orientation array, a polarization phase-shifting interferometer, which is showed in Fig. 6, is proposed based on the Twyman–Green interferometer. A continuous wave laser at 632.8 nm wavelength is used as a coherent light
P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
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Fig. 3. Fast axes of the azo-polymer film after each exposure.
Fig. 4. Fast axes of the azo-polymer orientation array.
Fig. 6. Optical setup for single-exposure polarization phase-shifting interferometer using the azo-polymer orientation array.
Fig. 5. The retardation uniformity of the azo-polymer orientation array measured by POM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
source. The polarization of the continuous wave laser makes a 45 degree angle with respect to optical axis of P1. The laser is incident upon a beam splitter (BS) splitting the laser into the reference beam and the object beam. Each beam passes through a polarizer (P1 or P2) and then is reflected by a reflecting mirror or object. The optical axis of P1 is parallel to the x-axis while the optical axis of P2 is parallel to the y-axis. The polarizer (P3) is placed before the CCD with its optical axis parallel to the x-axis. When the reference and object beam are combined again by BS, they become orthogonally polarized. The orthogonally polarized beams then pass through the azo-polymer orientation array placed at the conjugate image plane of the CCD. The mixing interferograms are acquired as a digital image sampled by 300 300 pixel, in which the CCD are composed of 480 640 pixel. During the adjustment of the interferometer, we block out the object beam, move the azo-polymer orientation array continuously, and then calculate the standard
deviation of the image acquired by the CCD along with the movement. When the standard deviation is maximized, the azopolymer orientation array is aligned to the CCD so that their pixels are accurately spatial matching. Each microretarder of a uint cell is imaged to a pixel of the CCD. The unit cell can be considered as a super-pixel. Let ar , ao , ϕ and δ denote the amplitude of the reference wave, the amplitude of the object beam, the phase differences between them and the retardation of microretarders, respectively. Referring to Fig. 7, using Jones matrix calculations [31], we have intensities I1, I2, I3 and I4 of four neighboring pixels of the interferogram given by ð1Þ I 1 ¼ M 2 þ N 2 2MN sin ϕ α I 2 ¼ M 2 þ N 2 þ 2MN sin ϕ α
I 3 ¼ M 2 þ N 2 2MN sin ϕ þ α
ð2Þ ð3Þ
I 4 ¼ M 2 þ N 2 þ 2MN sin ϕ þ α
ð4Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where M ¼ar cos 2 ðδ=2Þ þ ð1=4Þ sin ðδ=2Þ, pffiffiffi N ¼ ð 3=2Þao sin ðδ=2Þ, α ¼ arctan ð1=2Þ tan ðδ=2Þ . If an interferogram is captured, we obtain ϕ: 1 I4 I3 þ I2 I1 δ ð5Þ ϕ ¼ arctan tan 2 I4 I3 I2 þ I1 2 Here, it is assumed that the amplitude and the phase difference between the reference and object wavefront, ar , ao , ϕ have the same value of all four neighboring pixels. For all pixels on the interferogram,
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P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
this calculation is applied and we can obtain phase distributions of the object beam on the recording plane. Fig. 8 shows the data measured from the proposed polarization phase-shifting interferometer. Two flat mirrors are used as the reference and object objects, respectively. The angle between the mirrors are adjusted to generate several fringes of tilt. The image shows a magnified area of some pixels from the CCD array. The greyscale of the image corresponds to the measured intensity at each pixel. The high contrast between adjacent pixels demonstrates the ability to accomplish discrete spatial phase shifting at the pixel level. Every 4th pixel is combined to generate a continuous fringe map or interferogram. The synthetic fringe map shows excellent contrast across the whole array. By interpolating the data, lacking data in the intensity distribution can be complemented [11]. By this means, the measurement result has the same size with original array, although the actual spatial resolution cannot be increased by interpolation. According to the interferogram shown in Fig. 8, the wrapped phase differences between the object beam and reference beam can be determined by Eq. (5) and the corresponding result is shown in Fig. 9. The line profiles of the wrapped phase distributions in the 35th row and the 35th column are also shown in Fig. 8. From the above calculated results, we can come to the conclusion that the phase of the object beam is an oblique plane. This result is in accordance with the wavefront of the tilted mirror and the effectiveness of the proposed polarization phase-shifting interferometer using an azo-polymer orientation array is experimentally verified. However, the interference pattern shown in Fig. 9 is not completely straight mainly because of measurement errors. The unwrapped phase is obtained using a noniterative least-squares
Fig. 7. Intensity distribution of the mixing interferogram.
Fig. 9. The wrapped phase differences between the object wavefront and reference wavefront.
Fig. 10. Phase measurement error relative to fitted plane with least square method.
Fig. 8. Actual measurements made from the interferometer of Fig. 3. The Fringe pattern is synthesized by selecting every fourth pixel.
P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
algorithm, which is fitted into an ideal plane with least square method. The measurement error of the unwrapped phase relative to the ideal plane is calculated and shown in Fig. 10. The maximal measurement error is 0.13 rad. Because the accuracy of the interferometer bases on that all sub-pixels of the azo film have the same retardation, the nonuniformity of the azo-polymer orientation array plays an important role in the measurement error. Another source of error is the assumption that the phase difference between pixels remains constant over a small interval, which is valid only for wavefronts with small deviations [32]. 4. Conclusion In conclusion, we have presented a single-exposure polarization phase-shifting interferometer using an azo-polymer orientation array, which has been experimentally verified by measuring the interference of two plane mirrors. The method allows the use of ordinary recording devices and materials such as CCDs and azopolymer, and demonstrates a new application of azo-polymer in phase-shifting interferometer. The azo-polymer orientation array is easier to fabricate than wire-grid micro-polarizer array. The nonuniformity of the azo-polymer orientation array plays an important role in the measurement error, which should be fabricated with a quality as high as possible. Acknowledgement The authors acknowledge funding from the National Natural Science Foundation of China (NSFC) (grant no. 51303002) and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University. References [1] Zhang T, Yamaguchi I. Three-dimensional microscopy with phase-shifting digital holography. Opt Lett 1998;23:1221–3. [2] Servin M, Estrada JC, Medina O. Fourier transform demodulation of pixelated phase-masked interferograms. Opt Express 2010;18:16090–5. [3] Estrada JC, Servin M, Quiroga JA. Easy and straightforward construction of wideband phase-shifting algorithms for interferometry. Opt Lett 2009;34:413–5. [4] Smythe R, Moore R. Instantaneous phase measuring interferometry. Opt Eng 1984;23:361–4. [5] Hettwer A, Kranz J, Schwider J. Three channel phase-shifting interferometer using polarization-optics and a diffraction grating. Opt Eng 2000;39:960–6. [6] Freischlad K, Eng R, Hadaway JB. Interferometer for testing in vibration environments. Proc SPIE 2002:312. [7] Millerd J, Brock N, Hayes J, North-Morris M, Novak M, Wyant J. Pixelated phase-mask dynamic interferometer. Proc Soc Photo-Opt Instrum 2004;5531:304–14. [8] Novak M, Millerd J, Brock N, North-Morris M, Hayes J, Wyant J. Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer. Appl Opt 2005;44:6861–8. [9] Awatsuji Y, Sasada M, Kubota T. Parallel quasi-phase-shifting digital holography. Appl Phys Lett 2004;85:1069–71.
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[10] Brock NJ, Kimbrough BT, Millerd JE. A pixelated polarizer-based camera for instantaneous interferometric measurements. Polarization Sci Remote Sens V 2011;8160. [11] Suzuki H, Nomura T, Nitanai E, Numata T. Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method. Opt Rev 2010;17:176–80. [12] Huang JT, Wu S, Beckemper S, Gillner A, Zhang QJ, Wang KY. All-optical fabrication of ellipsoidal caps on azobenzene functional polymers. Opt Lett 2010;35:2711–3. [13] Fratz M, Sinzinger S, Giel D. Design and fabrication of polarization-holographic elements for laser beam shaping. Appl Opt 2009;48:2669–77. [14] Hrozhyk UA, Serak SV, Tabiryan NV, Hoke L, Steeves DM, Kimball BR. Azobenzene liquid crystalline materials for efficient optical switching with pulsed and/or continuous wave laser beams. Opt Express 2010;18:8697–704. [15] Nersisyan SR, Tabiryan NV, Steeves DM, Kimball BR, Chigrinov VG, Kwok HS. Study of azo dye surface command photoalignment material for photonics applications. Appl Opt 2010;49:1720–7. [16] Zhou JL, Shen J, Yang JJ, Ke Y, Wang KY, Zhang QJ. Fabrication of a pure polarization grating in a cross-linked azopolymer by polarization-modulated holography. Opt Lett 2006;31:1370–2. [17] Morikawa Y, Nagano S, Watanabe K, Kamata K, Iyoda T, Seki T. Optical alignment and patterning of nanoscale microdomains in a block copolymer thin film. Adv Mater 2006;18:883- þ. [18] Yager KG, Barrett CJ. Novel photo-switching using azobenzene functional materials. J Photochem Photobiol A 2006;182:250–61. [19] Patane S, Arena A, Allegrini M, Andreozzi L, Faetti M, Giordano M. Near-field optical writing on azo-polymethacrylate spin-coated films. Opt Commun 2002;210:37–41. [20] Liu ZQ, Srisanit N, Ke XJ, Wu PF, Song S, Yang JJ, et al. An azobenzene functionalized polymer for laser direct writing waveguide fabrication. Opt Commun 2007;273:94–8. [21] Lee S, Kang HS, Park JK. Directional photofluidization lithography: micro/ nanostructural evolution by photofluidic motions of azobenzene materials. Adv Mater 2012;24:2069–103. [22] Natansohn A, Rochon P, Gosselin J, Xie S. Azo polymers for reversible optical storage. 1. Poly [40 -[[2-(acryloyloxy) ethyl] ethylamino]-4-nitroazobenzene]. Macromolecules 1992;25:2268–73. [23] Yaroshchuk OV, Dumont M, Zakrevskyy YA, Bidna TV, Lindau J. Molecular structure of azopolymers and photoinduced 3D orientational order. 1. Azobenzene polyesters. J Phys Chem B 2004;108:4647–58. [24] Presnyakov V, Asatryan K, Galstian T. Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer. Opt Express 2006;14:10558–64. [25] Pan X, Xiao S, Wang C, Cai P, Lu X, Lu Q. Photoinduced anisotropy in an azocontaining ionic liquid–crystalline polymer. Opt Commun 2009;282:763–8. [26] Bian SP, He JA, Li L, Kumar J, Tripathy SK. Large photoinduced birefringence in azo dye/polyion films assembled by electrostatic sequential adsorption. Adv Mater 2000;12:1202–5. [27] Fu SC, Liu YC, Lu ZF, Dong L, Hu WL, Xie MG. Photo-induced birefringence and polarization holography in polymer films containing spirooxazine compounds pre-irradiated by UV light. Opt Commun 2004;242:115–22. [28] Fratz M, Giel DM, Fischer P. Digital polarization holograms with defined magnitude and orientation of each pixel’s birefringence. Opt Lett 2009;34:1270–2. [29] Liu J, Sun K, Li ZC, Gao JG, Su W, Yang J, et al. Banded texture of photo-aligned azobenzene-containing side-chain liquid crystalline polymers. Polymer 2004;45:4331–6. [30] Ruhmann R. Polymers for optical storage—photoresponsive polymers by structure variation in side-group polymethacrylates. Polym Int 1997;43:103–8. [31] Yan P, Wang K, Gao J. Polarization phase-shifting interferometer by rotating azo-polymer film with photo-induced optical anisotropy. Opt Lasers Eng 2015;64:12–6. [32] Kimbrough BT. Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors. Appl Opt 2006;45:4554–62.
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Single-exposure polarization phase-shifting interferometer using an azo-polymer orientation array Peizheng Yan a, Keyi Wang a, Pengcheng Cui a, Jiangang Gao b,n, Jiajun Ma c, Qijin Zhang c a
Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, Anhui, PR China School of Biological and Chemical Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui, PR China c Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei 230026, Anhui, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 5 December 2014 Received in revised form 25 March 2015 Accepted 17 April 2015
We propose a single-exposure polarization phase-shifting interferometer based on a beam-splitting method using an azo-polymer orientation array, which is prepared from an ordinary azo-polymer film with photo-induced optical anisotropy. The azo-polymer orientation array gives a four-step phase shift on the interferogram, from which phase differences between the orthogonal polarized reference and object beam can be calculated. Experimental results are provided to verify the feasibility of the proposed interferometer. The azo-polymer orientation array is easy to fabricate, making this method convenient and low-cost. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Azo-polymer film Photo-induced optical anisotropy Phase-shifting interferometer
1. Introduction Phase-shifting interferometry is an established method for measuring a variety of physical parameters ranging from the surface figure of mirrors to the displacement of solid objects [1]. It has become ubiquitous for the measurement and characterization of many types of surfaces including lenses, mirrors, and aspheres, with various techniques available for analyzing interference data [2,3]. Phase shifting of a wavefront can be accomplished by sequentially introducing a phase step (temporal phase shifting). The largest limitation of temporal phase shifting interferometry for optical testing is the sensitivity to the environment, both vibration and air turbulence. Vibration effects can be reduced by taking all the phase shifted frames simultaneously, which is also called spatial phase shifting. If the interferometer is insensitive to vibration, many measurements can be averaged to reduce the effects of air turbulence. A variety of methods for spatial phase shifting have been developed over the years. The most common ones are the use of multiple cameras to detect multiple interferograms [4], the use of diffractive elements to simultaneously image three or more images onto a single CCD [5] and the use of a tilted reference wave to introduce a spatial carrier frequency into the pattern [6]. The approach with multiple cameras tends to be expensive and difficult to implement. The diffraction approach relies on the diffractive elements, which are expensive and difficult to manufacture. The third method must utilize high precision optics to avoid introducing aberrations between the two non-common path beams.
n
Corresponding author. E-mail address: [email protected] (J. Gao).
http://dx.doi.org/10.1016/j.optlaseng.2015.04.011 0143-8166/& 2015 Elsevier Ltd. All rights reserved.
A far more robust and compact spatial phase-shifting method has been developed by Millerd et al. [7–9], in which a periodic phase-mask array of micro-polarizers is physically attached to a CCD sensor to obtain a unique phase-shift over each pixel. The micropolarizer arrays utilize Moxtek’s wiregrid polarizer technology, which utilizes nanoscale patterning to form a metal grating with sub-wavelength spacing on a thin transparent glass substrate [10]. The wiregrid micro-polarizer array is produced in a multistep lithographic process, which is complex and high-cost. In this paper, we propose a single-exposure phase-shifting interferometer using an azo-polymer orientation array, which is easier to fabricate and low-cost. The azo-polymer orientation array acts as a microretarder array by which different phase shifts are achieved at the pixel-by-pixel level on the interferogram [11]. Azobenzene and its derivatives are excellent photoresponsive materials that can be applied in many domains, including polarization filters, optical data storage, holography, photo-switching of optical elements and lithography [12–21]. The applications of azocontaining materials are based on the photoisomerization action of azochromophores [22] and photo-induced orientation is a remarkable property of azobenzene. Upon illumination with a linearly polarized light at wavelengths below the absorption edge, these azobenzene polymers undergo cycles of cis–trans isomerizations. Every time an azo chromophore undergoes a trans to cis to trans isomerization cycle, its position will vary slightly and randomly, which drive the molecules to align with their major axis perpendicularly to the polarization axis of the incident light [18,23,24]. A high polarizability along the long molecular axis of the azobenzene fragments in the trans conformation determines birefringence effects for the light outside the absorption band [25–27]. The refractive
76
P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
index (ne) for the light polarized along the long molecular axis is bigger than the refractive indices (no) in all directions perpendicular to the long molecular axis. Thus, if the polarization orientation of the writing light beam is controlled and can be changed in a well-defined way, it is possible to control the orientation of the birefringence in the polymer and generate space variant retarders. A remarkable aspect of the photoalignment process is that it saturates after enough illumination. If the beam intensity and the exposure time are chosen in a way that the polymer is exposed beyond the saturation, the birefringence is not further increased, which makes the azo-polymer orientation array easy to fabricate. Illumination above the absorption edge of the material does not affect the birefringence and it remains stable [13,28], allowing one to apply the birefringent polymer layer for polarization control.
2. Fabrication of azo-polymer orientation array The azo-polymer (abbreviated as PCN6) used in this part of the work is a conventional side-chain liquid crystalline polymethacrylate bearing azobenzene groups according to previous reports [29,30], of which the wavelength of optical absorption edge is ca. 550 nm. The chemical structure of PCN6 is shown in Fig. 1. A smooth PCN6 film was made by spin-coating with cyclopentanone as a solvent on a 2 cm 2 cm quartz substrate and dried under vacuum at room temperature for 3 days, then the thickness of the transparent film was measured on a Shimadzu UV-2550 UV–vis spectrophotometer to be about 2 μm. The experimental setup used to encode the birefringence in the photopolymer is depicted in Fig. 2. The laser beam at 405 nm is polarized parallel to the y-axis. Azimuth of laser polarization direction through the polarizer, the fast axis of electro-optic modulator and quarter-wave plate with respect to the y-axis are 0, π/4 and 0, respectively. The azo polymer film is mounted on a precision x–ymoving stage and located in the conjugate image plane of the photo mask. The projecting lens has a large aperture (F1.2) and a high resolution (150 lp/mm) and the square photomask and azo film are placed in the center of the lens filed to reduce the impact of diffraction. The photo mask uses a thin film of chrome as an opaque material, which is sputtering coated on Soda Lime glass. On the photo mask shown in Fig. 2, the black area is coated with chrome stopping the laser at 405 nm passing through the photo mask, while chrome in the white area is inductively coupled plasmas etched, with a transmittance value of 88% at 375–450 nm. The period of the photo mask, represented by ‘T’ in Fig. 2, is 50 μm. The magnification of the projection optical system is 0.4 , which means the actual period of the fabricated mask is 20 μm. Four exposures are needed to fabricate of the azo-polymer orientation array. First, set the polarization of the laser beam to π/ 3 by changing the voltage applied to the electro-optic modulator and illuminate the azo polymer for enough time untill it saturates. The exposure area is the projected image of the transparent area on photo mask. Second, move the azo polymer film along the xaxis by T/2, change the polarization of the laser beam to π/6, and illuminate the azo polymer film for enough time. In the third and fourth exposure, move the azo polymer film along the y-axis or xaxis by T/2, change the polarization of the laser beam to π/6 or
Fig. 2. Experimental setup for fabricating the azo-polymer orientation array.
π/3, and illuminate the azo polymer film for enough time again, which is similar to the second step. Because of photo-induced orientation of azobenzene groups, the fast axis of the azo-polymer is the same with the polarization of the laser controlled by the electro-optic modulator. The fast axis of the azo-polymer film after each exposure is shown in Fig. 3. The voltages applied to the electro-optic modulator to set the polarization of the laser beam to the four angles have been calibrated accurately to ensure the spatial variation of the azimuth angle of the optic axis. Only the central 3 mm 3 mm of the whole smooth PCN6 film is used to fabricate the azo-polymer mask, which ensures the uniformity of the film thickness of azo-polymer mask. When the azo polymer is illuminated for enough time until it is saturated, the phase retardation between its fast axis and slow axis reaches a special stable value, which depends on the thickness and chemical component of the film. Therefore, all exposed azo films have the same degree of retardation, which was measured to be 120 degree with the same azo film and laser in our previous work [31]. After four exposures, the azo-polymer is orientated periodically, forming an azo-polymer orientation array. A set of four (2 2) microretarders with the same retardation, whose fast axes have four different angles, are arranged into a “unit cell”, which is repeated continuously over the entire array. Fig. 4 illustrates a unit cell comprised of four microretarders. The retardation uniformity of the azo-polymer orientation array is measured by the polarizing optical microscopy (POM). When the azo-polymer orientation array is rotated to a certain angle, an image is captured by the POM, partly shown in Fig. 5. The line profiles of the retardation in the central row and the central column marked by the red line are also shown in Fig. 5. Although the borders between sub-pixels are blurred because of the diffraction, the retardation uniformity of the azo-polymer orientation array has a good quality of retardation uniformity.
3. Polarization phase-shifting interferometer using an azo-polymer orientation array
Fig. 1. Chemical structure of PCN6.
Using the fabricated azo-polymer orientation array, a polarization phase-shifting interferometer, which is showed in Fig. 6, is proposed based on the Twyman–Green interferometer. A continuous wave laser at 632.8 nm wavelength is used as a coherent light
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Fig. 3. Fast axes of the azo-polymer film after each exposure.
Fig. 4. Fast axes of the azo-polymer orientation array.
Fig. 6. Optical setup for single-exposure polarization phase-shifting interferometer using the azo-polymer orientation array.
Fig. 5. The retardation uniformity of the azo-polymer orientation array measured by POM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
source. The polarization of the continuous wave laser makes a 45 degree angle with respect to optical axis of P1. The laser is incident upon a beam splitter (BS) splitting the laser into the reference beam and the object beam. Each beam passes through a polarizer (P1 or P2) and then is reflected by a reflecting mirror or object. The optical axis of P1 is parallel to the x-axis while the optical axis of P2 is parallel to the y-axis. The polarizer (P3) is placed before the CCD with its optical axis parallel to the x-axis. When the reference and object beam are combined again by BS, they become orthogonally polarized. The orthogonally polarized beams then pass through the azo-polymer orientation array placed at the conjugate image plane of the CCD. The mixing interferograms are acquired as a digital image sampled by 300 300 pixel, in which the CCD are composed of 480 640 pixel. During the adjustment of the interferometer, we block out the object beam, move the azo-polymer orientation array continuously, and then calculate the standard
deviation of the image acquired by the CCD along with the movement. When the standard deviation is maximized, the azopolymer orientation array is aligned to the CCD so that their pixels are accurately spatial matching. Each microretarder of a uint cell is imaged to a pixel of the CCD. The unit cell can be considered as a super-pixel. Let ar , ao , ϕ and δ denote the amplitude of the reference wave, the amplitude of the object beam, the phase differences between them and the retardation of microretarders, respectively. Referring to Fig. 7, using Jones matrix calculations [31], we have intensities I1, I2, I3 and I4 of four neighboring pixels of the interferogram given by ð1Þ I 1 ¼ M 2 þ N 2 2MN sin ϕ α I 2 ¼ M 2 þ N 2 þ 2MN sin ϕ α
I 3 ¼ M 2 þ N 2 2MN sin ϕ þ α
ð2Þ ð3Þ
I 4 ¼ M 2 þ N 2 þ 2MN sin ϕ þ α
ð4Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where M ¼ar cos 2 ðδ=2Þ þ ð1=4Þ sin ðδ=2Þ, pffiffiffi N ¼ ð 3=2Þao sin ðδ=2Þ, α ¼ arctan ð1=2Þ tan ðδ=2Þ . If an interferogram is captured, we obtain ϕ: 1 I4 I3 þ I2 I1 δ ð5Þ ϕ ¼ arctan tan 2 I4 I3 I2 þ I1 2 Here, it is assumed that the amplitude and the phase difference between the reference and object wavefront, ar , ao , ϕ have the same value of all four neighboring pixels. For all pixels on the interferogram,
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this calculation is applied and we can obtain phase distributions of the object beam on the recording plane. Fig. 8 shows the data measured from the proposed polarization phase-shifting interferometer. Two flat mirrors are used as the reference and object objects, respectively. The angle between the mirrors are adjusted to generate several fringes of tilt. The image shows a magnified area of some pixels from the CCD array. The greyscale of the image corresponds to the measured intensity at each pixel. The high contrast between adjacent pixels demonstrates the ability to accomplish discrete spatial phase shifting at the pixel level. Every 4th pixel is combined to generate a continuous fringe map or interferogram. The synthetic fringe map shows excellent contrast across the whole array. By interpolating the data, lacking data in the intensity distribution can be complemented [11]. By this means, the measurement result has the same size with original array, although the actual spatial resolution cannot be increased by interpolation. According to the interferogram shown in Fig. 8, the wrapped phase differences between the object beam and reference beam can be determined by Eq. (5) and the corresponding result is shown in Fig. 9. The line profiles of the wrapped phase distributions in the 35th row and the 35th column are also shown in Fig. 8. From the above calculated results, we can come to the conclusion that the phase of the object beam is an oblique plane. This result is in accordance with the wavefront of the tilted mirror and the effectiveness of the proposed polarization phase-shifting interferometer using an azo-polymer orientation array is experimentally verified. However, the interference pattern shown in Fig. 9 is not completely straight mainly because of measurement errors. The unwrapped phase is obtained using a noniterative least-squares
Fig. 7. Intensity distribution of the mixing interferogram.
Fig. 9. The wrapped phase differences between the object wavefront and reference wavefront.
Fig. 10. Phase measurement error relative to fitted plane with least square method.
Fig. 8. Actual measurements made from the interferometer of Fig. 3. The Fringe pattern is synthesized by selecting every fourth pixel.
P. Yan et al. / Optics and Lasers in Engineering 73 (2015) 75–79
algorithm, which is fitted into an ideal plane with least square method. The measurement error of the unwrapped phase relative to the ideal plane is calculated and shown in Fig. 10. The maximal measurement error is 0.13 rad. Because the accuracy of the interferometer bases on that all sub-pixels of the azo film have the same retardation, the nonuniformity of the azo-polymer orientation array plays an important role in the measurement error. Another source of error is the assumption that the phase difference between pixels remains constant over a small interval, which is valid only for wavefronts with small deviations [32]. 4. Conclusion In conclusion, we have presented a single-exposure polarization phase-shifting interferometer using an azo-polymer orientation array, which has been experimentally verified by measuring the interference of two plane mirrors. The method allows the use of ordinary recording devices and materials such as CCDs and azopolymer, and demonstrates a new application of azo-polymer in phase-shifting interferometer. The azo-polymer orientation array is easier to fabricate than wire-grid micro-polarizer array. The nonuniformity of the azo-polymer orientation array plays an important role in the measurement error, which should be fabricated with a quality as high as possible. Acknowledgement The authors acknowledge funding from the National Natural Science Foundation of China (NSFC) (grant no. 51303002) and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University. References [1] Zhang T, Yamaguchi I. Three-dimensional microscopy with phase-shifting digital holography. Opt Lett 1998;23:1221–3. [2] Servin M, Estrada JC, Medina O. Fourier transform demodulation of pixelated phase-masked interferograms. Opt Express 2010;18:16090–5. [3] Estrada JC, Servin M, Quiroga JA. Easy and straightforward construction of wideband phase-shifting algorithms for interferometry. Opt Lett 2009;34:413–5. [4] Smythe R, Moore R. Instantaneous phase measuring interferometry. Opt Eng 1984;23:361–4. [5] Hettwer A, Kranz J, Schwider J. Three channel phase-shifting interferometer using polarization-optics and a diffraction grating. Opt Eng 2000;39:960–6. [6] Freischlad K, Eng R, Hadaway JB. Interferometer for testing in vibration environments. Proc SPIE 2002:312. [7] Millerd J, Brock N, Hayes J, North-Morris M, Novak M, Wyant J. Pixelated phase-mask dynamic interferometer. Proc Soc Photo-Opt Instrum 2004;5531:304–14. [8] Novak M, Millerd J, Brock N, North-Morris M, Hayes J, Wyant J. Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer. Appl Opt 2005;44:6861–8. [9] Awatsuji Y, Sasada M, Kubota T. Parallel quasi-phase-shifting digital holography. Appl Phys Lett 2004;85:1069–71.
79
[10] Brock NJ, Kimbrough BT, Millerd JE. A pixelated polarizer-based camera for instantaneous interferometric measurements. Polarization Sci Remote Sens V 2011;8160. [11] Suzuki H, Nomura T, Nitanai E, Numata T. Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method. Opt Rev 2010;17:176–80. [12] Huang JT, Wu S, Beckemper S, Gillner A, Zhang QJ, Wang KY. All-optical fabrication of ellipsoidal caps on azobenzene functional polymers. Opt Lett 2010;35:2711–3. [13] Fratz M, Sinzinger S, Giel D. Design and fabrication of polarization-holographic elements for laser beam shaping. Appl Opt 2009;48:2669–77. [14] Hrozhyk UA, Serak SV, Tabiryan NV, Hoke L, Steeves DM, Kimball BR. Azobenzene liquid crystalline materials for efficient optical switching with pulsed and/or continuous wave laser beams. Opt Express 2010;18:8697–704. [15] Nersisyan SR, Tabiryan NV, Steeves DM, Kimball BR, Chigrinov VG, Kwok HS. Study of azo dye surface command photoalignment material for photonics applications. Appl Opt 2010;49:1720–7. [16] Zhou JL, Shen J, Yang JJ, Ke Y, Wang KY, Zhang QJ. Fabrication of a pure polarization grating in a cross-linked azopolymer by polarization-modulated holography. Opt Lett 2006;31:1370–2. [17] Morikawa Y, Nagano S, Watanabe K, Kamata K, Iyoda T, Seki T. Optical alignment and patterning of nanoscale microdomains in a block copolymer thin film. Adv Mater 2006;18:883- þ. [18] Yager KG, Barrett CJ. Novel photo-switching using azobenzene functional materials. J Photochem Photobiol A 2006;182:250–61. [19] Patane S, Arena A, Allegrini M, Andreozzi L, Faetti M, Giordano M. Near-field optical writing on azo-polymethacrylate spin-coated films. Opt Commun 2002;210:37–41. [20] Liu ZQ, Srisanit N, Ke XJ, Wu PF, Song S, Yang JJ, et al. An azobenzene functionalized polymer for laser direct writing waveguide fabrication. Opt Commun 2007;273:94–8. [21] Lee S, Kang HS, Park JK. Directional photofluidization lithography: micro/ nanostructural evolution by photofluidic motions of azobenzene materials. Adv Mater 2012;24:2069–103. [22] Natansohn A, Rochon P, Gosselin J, Xie S. Azo polymers for reversible optical storage. 1. Poly [40 -[[2-(acryloyloxy) ethyl] ethylamino]-4-nitroazobenzene]. Macromolecules 1992;25:2268–73. [23] Yaroshchuk OV, Dumont M, Zakrevskyy YA, Bidna TV, Lindau J. Molecular structure of azopolymers and photoinduced 3D orientational order. 1. Azobenzene polyesters. J Phys Chem B 2004;108:4647–58. [24] Presnyakov V, Asatryan K, Galstian T. Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer. Opt Express 2006;14:10558–64. [25] Pan X, Xiao S, Wang C, Cai P, Lu X, Lu Q. Photoinduced anisotropy in an azocontaining ionic liquid–crystalline polymer. Opt Commun 2009;282:763–8. [26] Bian SP, He JA, Li L, Kumar J, Tripathy SK. Large photoinduced birefringence in azo dye/polyion films assembled by electrostatic sequential adsorption. Adv Mater 2000;12:1202–5. [27] Fu SC, Liu YC, Lu ZF, Dong L, Hu WL, Xie MG. Photo-induced birefringence and polarization holography in polymer films containing spirooxazine compounds pre-irradiated by UV light. Opt Commun 2004;242:115–22. [28] Fratz M, Giel DM, Fischer P. Digital polarization holograms with defined magnitude and orientation of each pixel’s birefringence. Opt Lett 2009;34:1270–2. [29] Liu J, Sun K, Li ZC, Gao JG, Su W, Yang J, et al. Banded texture of photo-aligned azobenzene-containing side-chain liquid crystalline polymers. Polymer 2004;45:4331–6. [30] Ruhmann R. Polymers for optical storage—photoresponsive polymers by structure variation in side-group polymethacrylates. Polym Int 1997;43:103–8. [31] Yan P, Wang K, Gao J. Polarization phase-shifting interferometer by rotating azo-polymer film with photo-induced optical anisotropy. Opt Lasers Eng 2015;64:12–6. [32] Kimbrough BT. Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors. Appl Opt 2006;45:4554–62.