- Email: [email protected]
Wide-angle Michelson interferometer based on LCoS
Optics Communications 292 (2013) 36–41
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Wide-angle Michelson interferometer based on LCoS Haiyang Gao a,b, Dengxin Hua a, Yuanhe Tang b,n, Xiangang Cao b, Hanchen Liu c, Wanli Jia b a b c
School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an 710048, China School of Science, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an 710048, China School of Science, Xi’an Polytechnic University, No. 19 South Jinhua Road, Xi’an 710048, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2012 Received in revised form 8 November 2012 Accepted 14 November 2012 Available online 5 December 2012
A wide-angle Michelson interferometer based on LCoS is proposed as a novel device with no moving part for effectively measuring the upper atmospheric temperature and wind. The testing experiment gives a sequence of interferograms which can be used for evaluating the performances of this device through an image processing. The maximum phase modulations of 2.13p and 1.58p for 532 nm and 633 nm respectively can cover the desired detection range. The OPD variations with regard to incident angle are within 0.59 wavelengths. The instrument visibilities of 0.226–0.146 for both wavelengths have the decreasing trends with regard to the increasing incident angles. The suggestions for improving performances are also given. The results have proved its effectiveness which can satisfy the requirements for atmospheric wind measurement. & 2012 Elsevier B.V. All rights reserved.
Keywords: Wide-angle Michelson interferometer Liquid crystals on silicon Upper atmospheric wind field measurement Phase measurement
1. Introduction Usage of optical Doppler Michelson interferometer (ODMI) technology to measure the atmospheric wind in mesosphere and lower thermosphere (MLT) has received an increasing interest in recent years. In this field, one frontier and challenging research is developing a solid interferometer with no moving parts. Historically, the wind imaging interferometer (WINDII), a spaceborne instrument launched in 1991, is the most successful application of this technology [1], and its results of observations have been reviewed from a perspective of 20 years in reference [2]. During the last two decades, other refined variants following WINDII have appeared successively for obtaining more stable measurements. The polarizing atmosphere Michelson interferometer (PAMI), a polarizing instrument, enables the optical path difference (OPD) to be changed by rotating a polarizer external to the interferometer [3]. The divided-mirror scanning technique can obtain four simultaneous phase-stepped images [4]. This method divides one of the MI mirror into quadrants and each quadrant is coated separately by l/4 of OPD from one quadrant to another. The waves Michelson interferometer (WAMI) employs a segmented MI mirror for simultaneous fringe sampling at different OPDs [5]. More recently, the Doppler asymmetric spatial heterodyne spectroscopy (DASH) uses two gratings as the mirrors [6]. One particular advantage of DASH is the ability to measure a rest
n
Corresponding author. Tel.: þ86 298 206 6357. E-mail address: [email protected] (Y. Tang).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.11.046
calibration line and at the same time observing the Doppler shifted line [7]. All these instruments possess their own characteristics in response to the measurement without moving parts, but also have some weaknesses such as the inapplicability in multi-wavelength. According to this requirement, we propose a wide-angle MI based on liquid crystals on silicon (LCoS) in this research to provide a potential and practical method which has its own distinctive characteristics. The LCoS operates in reflective mode and adopts the complexity of complementary metal oxide semiconductor (CMOS) integrated circuit technology [8]. Its advantages include high fill factor, high quality process technology for pixel mirror reflectivity, higher pixel number and wide response band of wavelength [9]. The phase-only modulation (POM), a special and useful function of LCoS, is capable of giving sufficient phase modulation with negligible amplitude modulation. It has found widespread use as spatial light modulators (SLM) in applications such as adaptive optics [10,11], optical communication [12] and optical metrology [13,14]. In previous works, we have carried out a preliminary calculation and analysis for setting a LCoS on the Sagnac interferometer [15]. Though, there are still a few difficulties which cannot be considered thoughtfully in theoretical method. The glass materials of heavy crown glass of PSKn2-type, for example, have expensive costs and are difficult for machining process that may hinder their extensive applications. Subsequently we gave a wide-angle Michelson interferometer (MI) with large air gap which is more practical as a result of the effective reduction in the size of the glass arms and constraint on material [16]. Thus, in this work, a real custom phase-only LCoS
H. Gao et al. / Optics Communications 292 (2013) 36–41
37
obtained from Beijing Real-light Technology Corp is used to combine with the wide-angle MI for achieving the phase scanning with no moving parts. This innovative combination possesses higher practicality and flexibility with different wavelengths. We describe the structure followed by testing experiments designed for deriving the modulation range, linearity and visibility. The image processing techniques are also involved. Due to the inherent constraints and limitations of commercial device, however, we suggest a few corresponding alterations and improvements which need to be made by the assistance from the manufacturer in further researches when implementing ultimate measurement for atmospheric wind.
(LC) material, and a CMOS circuit. Since most of these layers are very thin, only two layers, the glass layer (refractive index of n3 and thickness of d3) and LC (average refractive index of n4 and thickness of d4), have the ability to cause the main impact on optical performance. Because of the rectangular area of LCoS, an aperture stop of F6.8 mm needs to be placed onto the surface of LCoS. In this update version of MI, both the clear apertures of BS cube and glass arm of this new production are expanded as 48 48 mm2 in this work. An aperture stop of F6.8 mm, additionally, is set between fixed mirror and glass arm in order to reduce the effect on visibility of interferogram resulted from the flux difference between the two reflected beams. According to the novel structure and the similar mathematical principles in references [15,16], the general OPD can be calculated as:
2. The structure of wide-angle Michelson interferometer based on LCoS
Dy ¼ 2ðn1 d1 cos y1 n2 d2 cos y2 n3 d3 cos y3 n4 d4 cos y4 Þ
Using ODMI technology for measuring the atmospheric wind requires a critical alternation called field widening. When a single plate of glass with a suitable thickness is placed in one arm of the interferometer, the OPD variation with the incident angle, wavelength and temperature can be slowed down greatly. This transformation can gain the superiority over the ordinary Michelson interferometer (MI). Therefore, the large optical flux is suitable for detecting the weak airglow signal, while the large resolving power allows the Doppler shift caused by wind to be distinguished. Details for designing and optimizing such MI have been described in the previous papers [3,17,18]. In this research an upgrade version of the wide-angle MI in previous work [16] is used to combine the LCoS, and its structure is shown in Fig. 1. The wide-angle MI, as one of the two key devices in this work, is formed by a beamsplitter (BS) cube glued with a glass arm and a large air gap. The glass arm employs the H-K9L glass with refractive index of n1 as its material. The design of the air gap d2 of 29.45 mm in combination with the glass arm with size d1 of 44.45 mm can produce the desired OPD. The LCoS, as the other key device, has the resolution of 1024 768 with one square pixel size of 9 mm (total size of 9.215 6.915 mm2), and gray level of 8bit. Its internal structure consists of a few layers including a glass window, optical glues, indium tin oxides (ITO) glass, liquid crystal
d1 d2 d3 d4 ¼ 2ðn1 d1 n2 d2 n3 d3 n4 d4 Þsin2 y n1 n2 n3 n4 ! sin4 y d1 d2 d3 d4 4 n31 n32 n33 n34
ð1Þ
where y1, y2, y3, y4 are the incident angles at four interfaces shown in Fig. 1. By using the Snell law the angles y1, y2, y3, y4 can be converted into the four terms only containing the incident angle y for the first interface. The first term in Eq. (1) is independent of y and can be represented as the fixed OPD
Dy ¼ 2ðn1 d1 n2 d2 n3 d3 n4 d4 Þ
ð2Þ
The fixed OPD is the most important value for a wide-angle MI, because it can determine both the wind and temperature measurement accuracies. Taking all the real parameters into Eq. (2), we can obtain the fixed OPDs of the wide-angle MI based on LCoS as 76.38 mm and 76.01 mm for wavelengths of 532 nm and 633 nm respectively. Theoretically, the spectral resolving powers R can reach 1.44 105 (532 nm) and 1.20 105 (633 nm) according to the function R¼ Dm/l (Dm denotes the maximum OPDs and l is wavelength) [18]. Thus, the superiority of this solid glass wide-angle MI may gain over the ordinary MI in air with the value ofpffiffiffiffiffiffi 814 (532 nm) and 742 (633 nm) based on the equation of n 2R, where n is the refractive index of glass [18].
3. Experiment
Fig. 1. The structure of the wide-angle MI based on LCoS. The wide-angle MI is formed by a BS cube glued with a glass arm and a large air gap. The design of the H-K9L glass arm with size of 44.45 mm in combination with the air gap of 29.45 mm can generate the required OPD. The LCoS has the resolution of 1024 768 with one square pixel size of 9 mm (total size of 9.215 6.915 mm2), and gray level of 8-bit. An aperture stop of F6.8 mm is placed onto the surface of LCoS. Another same aperture stop is set between fixed mirror and glass arm in order to reduce the effect on modulation of interferogram resulted from the flux difference between the two reflected beams.
The LCoS used here aims to provide phase stepping over approximate one fringe of the interferogram. Thus whether the modulation range of LCoS can cover the minimum requirement of 1.5p is the main performance to be tested. Other parameters, including the achromatic ability, linearity, stepped accuracy and visibility, are also need to be obtained by testing experiments. Fig. 2 shows the schematic diagram of the experimental setup and some imaging examples. The diffuse light from a planar light source, generated by an integrating sphere, is collimated and polarized by the combined lens 1 and polarizer 1 in turn. One beam reflected from BS enters the LCoS while the other beam penetrating BS and glass arm reaches the fixed mirror. Then passing through the polarizer 2 and the combined lens 2, the interference pattern can be generated and imaged on the CCD sensor. This camera permits CCD sensor to be operated at temperature of approximately 45 1C below the ambient temperature, and it has the resolution of 512 512, one pixel size of 20 mm, and the gray level of 16-bit. In order to produce a maximum incident angle of 3.91 at interferometer, we use two combined lenses 1 and 2 to form desired focal lengths. The combined lens 1 has a focal length of 72.5 mm and aperture of F50 mm, which is combined with two same coaxial lenses set with a certain interval. By the similar
38
H. Gao et al. / Optics Communications 292 (2013) 36–41
Fig. 2. The schematic diagram of experimental setup and imaging examples. The pictures at upper left corner are the photos for this experimental setup and two key devices. This system is calculated and optimized by the Code V software, so the impacts caused by the aberration on experimental result can be minimized. The lower images are the imaging examples.
means, the combined lens 2 is formed with a focal length of 72.5 mm and aperture of F50 mm. Due to these two appropriate focal lengths, the planar source with a diameter of 22 mm limited by a simple diaphragm can be imaged on the CCD sensor with a full utilization. The achromatic doublets are employed in this experimental system to reduce aberrations introduced by spherical surfaces. We also use the optical design software Code V to simulate and optimize this optical system, and obtain involved parameters. The aberration results are also derived and evaluated, the modulation transfer function (MTF) values within 0.6–0.8 at 0–25 lp/mm and the spot diagram size of about 19 mm indicate a satisfaction for the high-quality imaging. It is hoped that the impact caused by the aberration on test result can be minimized as much as possible. For obtaining the desired parameters, each complete experiment is divided into four steps as follows:
This step aims to find the flat field coefficient for each pixel. Thus, the LCoS is removed from this system for eliminating the interference, 50 images are shot at the same exposure time as mentioned in step (1) to obtain the flat-field calibration images. (3) Dark noise calibration: In order to subtract the dark noise from the original images, we close the shutter of CCD camera, and shoot 100 dark images with the same exposure time as mentioned in steps (1) and (2). (4) Achromatic performance: The He–Ne laser is replaced by a green DPSS laser (532 nm). Moving the LCoS towards the beam splitter cube by the electric moving platform, the air gap is adjusted to 44.35 mm. By repeating the operations of steps (1–3), a series of the same type of images can be obtained with the wavelength of 532 nm for the analysis of achromatic performance.
(1) Phase modulation performance: A He–Ne laser (633 nm) entering the integrated sphere is used to produce a planar light source. Through this entire optical system, 256 images are shot successively as the gray levels of LCoS changed from 0 to 255 in scanning interval of one. The CCD sensor works at 25.070.1 1C with exposure time of 0.20 s. (2) Flat-field calibration: When the planar light source enters an ordinary optical system, the vignetting could occur since the light flux has a decrease with the increasing off-axis angle.
4. Image processing Before analysis of performance, an image processing is carried out as shown in Fig. 3. The averaged dark noise image firstly needs to be obtained by averaging the 100 original dark images from step (3). This image is used to be subtracted by the original interferograms from step (1) and flat field images from step (2). The flat field calibration plays an important role in this optical system for analysis of performance. There are few factors that may
H. Gao et al. / Optics Communications 292 (2013) 36–41
39
Fig. 3. The image processing. All original images from the experiment need to be operated by this process to generate the qualified images for analysis of instrument performance. The flat-field calibration is an important step which can reduce adverse effects from the luminous flux variation with regard to the incident angle.
let a uniform planar source at object plane be an uneven image with dark edge through the system. This is mainly attributed to the decrease in the light flux with increasing incident angle. The changing reflectance of LCoS regarding to incident angle may be also a reason. Additionally, the tiny non-collimated optical system may cause the uneven distribution of the light intensities. Thus, in order to recover the standard flat field image, we carry out a consequent process by averaging the 50 original images from the flat field calibration testing, removing the noise, and smoothing by using a square array of 3 3 neighboring pixels. Reading out the gray levels of all pixels, and storing them in a matrix, the standard flat field image can be converted into the matrix form. Finding the max value of this matrix, and all the other values divided by this max value can give the flat-field coefficient matrix in which all the values are less than unit. Subsequently, all the original images derived from step (1) need to subtract the dark noise separately and are smoothed by using a square array of 3 3 neighboring pixels. Using the matrixes converted by these processed images to multiply the flat-field coefficient matrix mentioned above, we can finally obtain the qualified images for analysis of instrument performance.
5. Results and discussion 5.1. Phase modulation range and linearity Before the analysis, the fringe center in each processed image needs to be determined by calculating the extremum of a Gaussian fitting curve to the horizontal and vertical cross sections of the image. Sampling 20 images by an equal interval from one complete experiment, we ultimately identify an averaged center pixel number of (245, 260). Then the value by averaging the 25 neighboring pixels around the center pixel is calculated as the center value of one image. Fig. 4(b) shows the central values of all images drawn with regard to gray levels (or image serial numbers) as discrete dots for 532 nm. The solid line is the sine fitting curve for the discrete dots by least square means with adjusted R-square value of 0.948. The fitting curve is also a calibration for relationship between the gray level and the phase variation for analysis in next section. For the more convenient analysis,
Fig. 4. The phase modulation and linearity results. (a) The linearity and maximum range of phase modulation for 532 nm. (b) The sine calibration curve according to the relationship between gray values of LCoS and image for 532 nm. It indicates the maximum phase modulation of 6.699 rad (about 2.13p) and the modulation interval of 0.026 rad based on this 8-bit LCoS.
the fitting curve needs to be converted into a standard line by the linearization as shown in Fig. 4(a), and the deviations are drawn as discrete dots. This result indicates the maximum phase modulation of 6.699 rad (about 2.13p) and the modulation interval of 0.026 rad based on this 8-bit LCoS for 532 nm. Fig. 5 shows the same phase modulation information as Fig. 4 but with the wavelength of 633 nm. The solid line is also the sine fitting curve with adjusted R-square value of 0.978. From the perspective of the comparison, the result in Fig. 5(a) indicates that the maximum modulation of 4.951 rad (about 1.58p) for 633 nm is less than the value for 532 nm, so the modulation interval increases to 0.019 rad for each one gray level. This changing trend agrees with the description from the manufacturer. The data stability and linearity for 633 nm are slightly better than that for 532 nm. Since that the principle of ‘‘four-point algorithm’’ for wind measurement only requires the maximum modulation of 1.5p [17], the results in this section demonstrate the basic ability to cover this range if two significant airglow emission lines of OI (557.7 nm) and OI (630.0 nm) are employed. 5.2. OPD variation and instrument visibility In order to analyze the OPD variation with regard to the incident angle, we take one representative image to implement the calculation. For making full use of all the information of the whole image, the image is divided into several cycles with the width of one pixel from fringe center to edge. Based on the relations from the fitting curves of Figs. 4(b) and 5(b), the gray
40
H. Gao et al. / Optics Communications 292 (2013) 36–41
Fig. 6. The OPD variations with regard to incident angle. Green discrete spots and black solid line are experiment data and theoretical curve respectively for 532 nm. Red discrete spots and blue solid line are experiment data and theoretical curve respectively for 633 nm. (b) The instrument visibility variations with regard to incident angle for 532 nm (green spots) and 633 nm (red spots). For 532 nm the OPD variation at incident angle of 3.61 is 0.59 wavelengths, while the value for 633 nm is 0.50 wavelengths. The maximum difference of only 0.09 wavelengths between these two curves suggests the good achromatic ability. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The phase modulation and linearity results. (a) The linearity and maximum range of phase modulation for 633 nm. (b) The sine calibration curve according to the relationship between gray values of LCoS and image for 633 nm. It indicates the maximum phase modulation of 4.951 rad (about 1.58p) and the modulation interval of 0.019 rad based on this 8-bit LCoS.
level by averaging all pixels in each cycle can be corresponded to the phase shift from fringe center. Since each cycle has a linear relation to incident angle, the OPD variation with incident angle can be obtained by a conversion shown in Fig. 6. For 532 nm, the OPD variation at incident angle of 3.61 is 0.59 wavelengths, while the value for 633 nm is 0.50 wavelengths. The maximum difference of only 0.09 wavelengths between these two curves suggests the good achromatic ability. When the incident angle is less than 0.81, the instability of gray values appears in both curves. The random noise of CCD may be charged with the primary responsibility for this deviation due to the fewer pixels in the circle near the fringe center. The apparent visibility is a product of the emission line visibility and instrument visibility. The emission line visibility can be used for deriving temperature, since the spectral line broadening has a strong dependence of temperature. While, the apparent visibility has a significant impact on the signal-to-noise ratio (SNR) of the image, and it may also affect the accuracy for deriving wind. In this analysis, the spectral line visibility is considered as a known quantity because of the selected laser source, and the apparent visibility can be calculated by the fringe amplitude. Thus, we can obtain the instrument visibility from the apparent visibility divided by the spectral line visibility. With the same operation as shown in Figs. 4(b) and 5(b), 12 square bins of 5 5 pixels are sampled from center to edge in each image with an equal interval. Although the range of 0.226–0.191 for 532 nm is overall higher than that of 0.204–0.146 for 633 nm, as seen
Fig. 7. The instrument visibility variations with regard to incident angle. The instrument visibility variations with regard to incident angle for 532 nm (green spots) and 633 nm (red spots). The range of 0.226–0.191 for 532 nm is overall higher than that of 0.204–0.146 for 633 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from the results in Fig. 7, all the values are slightly lower than that are expected. At normal incidence the reflectivity of LCoS for 532 nm is only 62%, while the value of fixed mirror coated with silver is about 95%. The difference between two reflectivity values could impact on the light intensities from two arm of interferometer, and therefore reduce the instrument visibility by a factor of 10% at least. The reflectivity of 53% for 633 nm could make the visibility lower than that for 532 nm. The decreasing trend of visibility with regard to the increasing incident angle attributes to the same variation trend in the reflectivity of LCoS with incident angle. Furthermore, some other aspects, such as the wave front error of the manufactured optics and the polarization effects of the beam splitter and polarizers, could impact on the instrument visibility to some extent [19].
H. Gao et al. / Optics Communications 292 (2013) 36–41
5.3. Discussions From the results above, it seems obvious that the LCoS depends strongly on the wavelength. The shorter wavelength may prefer to provide modulation range with a higher value. While the decreasing wave front error with increasing wavelength may lead to more stability and consistency of data. This deduction has a consistency with the description in reference [20]. From a comprehensive view, however, the LCoS is more suitable for the wavelength of 557.7 nm emitted from O(1S) of airglow emission rather than for 630.0 nm from O(1D). As seen from Figs. 4(b) and 5(b), when the incident angle is in the range of 0.8–3.61, there are still small discrepancies. The fringe superposition of inevitable multiple reflections among the optical surfaces such as the polarizers and mirrors, and the wave front error making the fringe shape become nonsinusoidal, are considered as the main reasons, even though we have set the polarizers to be tilted by a small angle [19]. In addition, Figs. 4–6 show the phase fluctuations. The power instability of two lasers may be a partial reason. The main reason seems to be attributed to the electronic addressing of the liquid crystal by pulse modulation [21]. This weakness can be effectively reduced by the former analog LC-SLM technology to decrease the low frequency fluctuations [8], and by using polarizing state generators [20] or controlling temperature [22]. Although the application of LCoS in wide-angle MI can satisfy the basic requirements for wind measurement, it still has some inadequacies to be improved. The higher phase modulation accuracy requires more stability of the electrical components in LCoS. To increase the instrument visibility, reducing the reflectance of fixed mirror to the same level as LCoS may be a more effective method rather than increasing fill factor of LCoS. Since the LCoS works at polarized state, the light throughput has been weakened a lot before arriving at CCD sensor. Thus, if the very weak airglow emissions are employed as the targets, we must expand the effective area of LCoS in order to enhance the e´tendue and responsivity of the optical system. Also, only the sufficient large e´tendue makes it possible to simultaneously implement four phase steps as mentioned in reference [15]. While, this very potential method involves a complex separated imaging system and more technical challenges, and how to realize this concept has been determined as the focal research in our further work.
6. Conclusions In summary, we have proposed a wide-angle MI based on LCoS as a stepping device with no moving part to provide an effective technique for upper atmospheric wind measurement. The experiment are designed and operated to obtain a sequence of interferograms. By the image processing and analysis, the results indicate the maximum phase modulations of 2.13p for 532 nm and 1.58p for 633 nm can cover the necessary detection range.
41
The OPD variations with regard to incident angle for both wavelengths are within 0.59 wavelengths, while the instrument visibilities of 0.226–0.191 for 532 nm and 0.204–0.146 for 633 nm still need to be improved in the further work. The phase fluctuations are mainly attributed to the multiple reflections, the wave front error, the electronic addressing by pulse modulation and the power instability of the lasers. We also give the aspects for improving performance. Though, this novel device has been proved its effectiveness, and we hope that it can provide an innovative way for the research field.
Acknowledgments The authors would like to thank the support by the National Natural Science Foundation of China (Nos. 10874138, 41027004 and 61275185), the Education Office of Shaanxi Province (No. 09JK653), and the Excellent Doctoral Dissertation Fund of Xi’an University of Technology (No. 101-211104).
References [1] G. Shepherd, G. Thuillier, W. Gault, B. Solheim, C. Hersom, J. Alunni, et al., Journal of Geophysical Research 98 (1993) 10725. [2] G. Shepherd, G. Thuillier, Y. Cho, M. Duboin, W. Evans, W. Gault, et al., Reviews of Geophysics 50 (RG2007) (2012) 1. [3] J.C. Bird, F. Liang, B.H. Solheim, G.G. Shepherd, Measurement Science & Technology 6 (1995) 1368. [4] W. Gault, S. Sargoytchev, S. Brown, Proceedings of SPIE 4306 (2001) 266. [5] W.E. Ward, W.A. Gault, G.G. Shepherd, N. Rowlands, Proceedings of SPIE 4540 (2001) 100. [6] C. Englert, D. Babcock, J.M. Harlander, Applied Optics 46 (2007) 7297. [7] J. Harlander, C. Englert, D. Babcock, F.L. Roesler, Optics Express 18 (2010) 26430. [8] N. Collings, T. Davey, J. Christmas, D. Chu, B. Crossland., Journal of Display Technology 7 (2011) 112. [9] S.T. Wu, D.K. Yang, Reflective Liquid Crystal Displays, John Wiley & Sons Inc., Chichester, 2005. [10] H. Dai, K. Xu, Y. Liu, X. Wang, J. Liu, Optics Communications 238 (2004) 269. [11] Z. Cao, Q. Mu, L. Hu, D. Li, Z. Peng, Y. Liu, et al., Optics Express 17 (2009) 2530. [12] D. Sinefeld, D. Marom, Optics Letters 37 (2012) 1. [13] W. Osten, C. Kohler, J. Liesener, Journal of Optics A: Pure and Applied Optics 38 (2005) 71. [14] F. Bai, F. Han, Y. Xu, X. Bao, S. Gan, Optics and Lasers in Engineering 49 (2011) 932. [15] H. Gao, Y. Tang, D. Hua, L. Qin, C. Zhu, Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 268. [16] H. Gao, Y. Tang, D. Hua, H. Liu, Applied Optics 50 (2011) 5655. [17] G. Shepherd, W. Gault, D. Miller, Z. Pasturczyk, S. Johnston, P. Kosteniuk, et al., Applied Optics 24 (1985) 1571. [18] G. Shepherd, Spectral Imaging of the Atmosphere, Academic Press, New York, 2003, pp. 133–134, pp. 146–147, pp. 175–180. [19] W.E. Ward, Z. Pasturczyk, W.A. Gault, G.G. Shepherd, Applied Optics 24 (1985) 1589. [20] A. Lizana, A. Ma´rquez, I. Moreno, C. Iemmi, J. Campos, M. Yzuel, Journal of the European Optical Society—Rapid Publications 3 (2008) 08011. [21] J. Moore, N. Collings, W. Crossland, A. Davey, M. Evans, A. Jeziorska, et al., IEEE Photonics Technology Letters 20 (2008) 60. [22] J. Garcı´a-Ma´rquez, V. Lo´pez, A. Gonza´lez-Vega, E. Noe´, Optics Express 20 (2012) 8431.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Wide-angle Michelson interferometer based on LCoS Haiyang Gao a,b, Dengxin Hua a, Yuanhe Tang b,n, Xiangang Cao b, Hanchen Liu c, Wanli Jia b a b c
School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an 710048, China School of Science, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an 710048, China School of Science, Xi’an Polytechnic University, No. 19 South Jinhua Road, Xi’an 710048, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2012 Received in revised form 8 November 2012 Accepted 14 November 2012 Available online 5 December 2012
A wide-angle Michelson interferometer based on LCoS is proposed as a novel device with no moving part for effectively measuring the upper atmospheric temperature and wind. The testing experiment gives a sequence of interferograms which can be used for evaluating the performances of this device through an image processing. The maximum phase modulations of 2.13p and 1.58p for 532 nm and 633 nm respectively can cover the desired detection range. The OPD variations with regard to incident angle are within 0.59 wavelengths. The instrument visibilities of 0.226–0.146 for both wavelengths have the decreasing trends with regard to the increasing incident angles. The suggestions for improving performances are also given. The results have proved its effectiveness which can satisfy the requirements for atmospheric wind measurement. & 2012 Elsevier B.V. All rights reserved.
Keywords: Wide-angle Michelson interferometer Liquid crystals on silicon Upper atmospheric wind field measurement Phase measurement
1. Introduction Usage of optical Doppler Michelson interferometer (ODMI) technology to measure the atmospheric wind in mesosphere and lower thermosphere (MLT) has received an increasing interest in recent years. In this field, one frontier and challenging research is developing a solid interferometer with no moving parts. Historically, the wind imaging interferometer (WINDII), a spaceborne instrument launched in 1991, is the most successful application of this technology [1], and its results of observations have been reviewed from a perspective of 20 years in reference [2]. During the last two decades, other refined variants following WINDII have appeared successively for obtaining more stable measurements. The polarizing atmosphere Michelson interferometer (PAMI), a polarizing instrument, enables the optical path difference (OPD) to be changed by rotating a polarizer external to the interferometer [3]. The divided-mirror scanning technique can obtain four simultaneous phase-stepped images [4]. This method divides one of the MI mirror into quadrants and each quadrant is coated separately by l/4 of OPD from one quadrant to another. The waves Michelson interferometer (WAMI) employs a segmented MI mirror for simultaneous fringe sampling at different OPDs [5]. More recently, the Doppler asymmetric spatial heterodyne spectroscopy (DASH) uses two gratings as the mirrors [6]. One particular advantage of DASH is the ability to measure a rest
n
Corresponding author. Tel.: þ86 298 206 6357. E-mail address: [email protected] (Y. Tang).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.11.046
calibration line and at the same time observing the Doppler shifted line [7]. All these instruments possess their own characteristics in response to the measurement without moving parts, but also have some weaknesses such as the inapplicability in multi-wavelength. According to this requirement, we propose a wide-angle MI based on liquid crystals on silicon (LCoS) in this research to provide a potential and practical method which has its own distinctive characteristics. The LCoS operates in reflective mode and adopts the complexity of complementary metal oxide semiconductor (CMOS) integrated circuit technology [8]. Its advantages include high fill factor, high quality process technology for pixel mirror reflectivity, higher pixel number and wide response band of wavelength [9]. The phase-only modulation (POM), a special and useful function of LCoS, is capable of giving sufficient phase modulation with negligible amplitude modulation. It has found widespread use as spatial light modulators (SLM) in applications such as adaptive optics [10,11], optical communication [12] and optical metrology [13,14]. In previous works, we have carried out a preliminary calculation and analysis for setting a LCoS on the Sagnac interferometer [15]. Though, there are still a few difficulties which cannot be considered thoughtfully in theoretical method. The glass materials of heavy crown glass of PSKn2-type, for example, have expensive costs and are difficult for machining process that may hinder their extensive applications. Subsequently we gave a wide-angle Michelson interferometer (MI) with large air gap which is more practical as a result of the effective reduction in the size of the glass arms and constraint on material [16]. Thus, in this work, a real custom phase-only LCoS
H. Gao et al. / Optics Communications 292 (2013) 36–41
37
obtained from Beijing Real-light Technology Corp is used to combine with the wide-angle MI for achieving the phase scanning with no moving parts. This innovative combination possesses higher practicality and flexibility with different wavelengths. We describe the structure followed by testing experiments designed for deriving the modulation range, linearity and visibility. The image processing techniques are also involved. Due to the inherent constraints and limitations of commercial device, however, we suggest a few corresponding alterations and improvements which need to be made by the assistance from the manufacturer in further researches when implementing ultimate measurement for atmospheric wind.
(LC) material, and a CMOS circuit. Since most of these layers are very thin, only two layers, the glass layer (refractive index of n3 and thickness of d3) and LC (average refractive index of n4 and thickness of d4), have the ability to cause the main impact on optical performance. Because of the rectangular area of LCoS, an aperture stop of F6.8 mm needs to be placed onto the surface of LCoS. In this update version of MI, both the clear apertures of BS cube and glass arm of this new production are expanded as 48 48 mm2 in this work. An aperture stop of F6.8 mm, additionally, is set between fixed mirror and glass arm in order to reduce the effect on visibility of interferogram resulted from the flux difference between the two reflected beams. According to the novel structure and the similar mathematical principles in references [15,16], the general OPD can be calculated as:
2. The structure of wide-angle Michelson interferometer based on LCoS
Dy ¼ 2ðn1 d1 cos y1 n2 d2 cos y2 n3 d3 cos y3 n4 d4 cos y4 Þ
Using ODMI technology for measuring the atmospheric wind requires a critical alternation called field widening. When a single plate of glass with a suitable thickness is placed in one arm of the interferometer, the OPD variation with the incident angle, wavelength and temperature can be slowed down greatly. This transformation can gain the superiority over the ordinary Michelson interferometer (MI). Therefore, the large optical flux is suitable for detecting the weak airglow signal, while the large resolving power allows the Doppler shift caused by wind to be distinguished. Details for designing and optimizing such MI have been described in the previous papers [3,17,18]. In this research an upgrade version of the wide-angle MI in previous work [16] is used to combine the LCoS, and its structure is shown in Fig. 1. The wide-angle MI, as one of the two key devices in this work, is formed by a beamsplitter (BS) cube glued with a glass arm and a large air gap. The glass arm employs the H-K9L glass with refractive index of n1 as its material. The design of the air gap d2 of 29.45 mm in combination with the glass arm with size d1 of 44.45 mm can produce the desired OPD. The LCoS, as the other key device, has the resolution of 1024 768 with one square pixel size of 9 mm (total size of 9.215 6.915 mm2), and gray level of 8bit. Its internal structure consists of a few layers including a glass window, optical glues, indium tin oxides (ITO) glass, liquid crystal
d1 d2 d3 d4 ¼ 2ðn1 d1 n2 d2 n3 d3 n4 d4 Þsin2 y n1 n2 n3 n4 ! sin4 y d1 d2 d3 d4 4 n31 n32 n33 n34
ð1Þ
where y1, y2, y3, y4 are the incident angles at four interfaces shown in Fig. 1. By using the Snell law the angles y1, y2, y3, y4 can be converted into the four terms only containing the incident angle y for the first interface. The first term in Eq. (1) is independent of y and can be represented as the fixed OPD
Dy ¼ 2ðn1 d1 n2 d2 n3 d3 n4 d4 Þ
ð2Þ
The fixed OPD is the most important value for a wide-angle MI, because it can determine both the wind and temperature measurement accuracies. Taking all the real parameters into Eq. (2), we can obtain the fixed OPDs of the wide-angle MI based on LCoS as 76.38 mm and 76.01 mm for wavelengths of 532 nm and 633 nm respectively. Theoretically, the spectral resolving powers R can reach 1.44 105 (532 nm) and 1.20 105 (633 nm) according to the function R¼ Dm/l (Dm denotes the maximum OPDs and l is wavelength) [18]. Thus, the superiority of this solid glass wide-angle MI may gain over the ordinary MI in air with the value ofpffiffiffiffiffiffi 814 (532 nm) and 742 (633 nm) based on the equation of n 2R, where n is the refractive index of glass [18].
3. Experiment
Fig. 1. The structure of the wide-angle MI based on LCoS. The wide-angle MI is formed by a BS cube glued with a glass arm and a large air gap. The design of the H-K9L glass arm with size of 44.45 mm in combination with the air gap of 29.45 mm can generate the required OPD. The LCoS has the resolution of 1024 768 with one square pixel size of 9 mm (total size of 9.215 6.915 mm2), and gray level of 8-bit. An aperture stop of F6.8 mm is placed onto the surface of LCoS. Another same aperture stop is set between fixed mirror and glass arm in order to reduce the effect on modulation of interferogram resulted from the flux difference between the two reflected beams.
The LCoS used here aims to provide phase stepping over approximate one fringe of the interferogram. Thus whether the modulation range of LCoS can cover the minimum requirement of 1.5p is the main performance to be tested. Other parameters, including the achromatic ability, linearity, stepped accuracy and visibility, are also need to be obtained by testing experiments. Fig. 2 shows the schematic diagram of the experimental setup and some imaging examples. The diffuse light from a planar light source, generated by an integrating sphere, is collimated and polarized by the combined lens 1 and polarizer 1 in turn. One beam reflected from BS enters the LCoS while the other beam penetrating BS and glass arm reaches the fixed mirror. Then passing through the polarizer 2 and the combined lens 2, the interference pattern can be generated and imaged on the CCD sensor. This camera permits CCD sensor to be operated at temperature of approximately 45 1C below the ambient temperature, and it has the resolution of 512 512, one pixel size of 20 mm, and the gray level of 16-bit. In order to produce a maximum incident angle of 3.91 at interferometer, we use two combined lenses 1 and 2 to form desired focal lengths. The combined lens 1 has a focal length of 72.5 mm and aperture of F50 mm, which is combined with two same coaxial lenses set with a certain interval. By the similar
38
H. Gao et al. / Optics Communications 292 (2013) 36–41
Fig. 2. The schematic diagram of experimental setup and imaging examples. The pictures at upper left corner are the photos for this experimental setup and two key devices. This system is calculated and optimized by the Code V software, so the impacts caused by the aberration on experimental result can be minimized. The lower images are the imaging examples.
means, the combined lens 2 is formed with a focal length of 72.5 mm and aperture of F50 mm. Due to these two appropriate focal lengths, the planar source with a diameter of 22 mm limited by a simple diaphragm can be imaged on the CCD sensor with a full utilization. The achromatic doublets are employed in this experimental system to reduce aberrations introduced by spherical surfaces. We also use the optical design software Code V to simulate and optimize this optical system, and obtain involved parameters. The aberration results are also derived and evaluated, the modulation transfer function (MTF) values within 0.6–0.8 at 0–25 lp/mm and the spot diagram size of about 19 mm indicate a satisfaction for the high-quality imaging. It is hoped that the impact caused by the aberration on test result can be minimized as much as possible. For obtaining the desired parameters, each complete experiment is divided into four steps as follows:
This step aims to find the flat field coefficient for each pixel. Thus, the LCoS is removed from this system for eliminating the interference, 50 images are shot at the same exposure time as mentioned in step (1) to obtain the flat-field calibration images. (3) Dark noise calibration: In order to subtract the dark noise from the original images, we close the shutter of CCD camera, and shoot 100 dark images with the same exposure time as mentioned in steps (1) and (2). (4) Achromatic performance: The He–Ne laser is replaced by a green DPSS laser (532 nm). Moving the LCoS towards the beam splitter cube by the electric moving platform, the air gap is adjusted to 44.35 mm. By repeating the operations of steps (1–3), a series of the same type of images can be obtained with the wavelength of 532 nm for the analysis of achromatic performance.
(1) Phase modulation performance: A He–Ne laser (633 nm) entering the integrated sphere is used to produce a planar light source. Through this entire optical system, 256 images are shot successively as the gray levels of LCoS changed from 0 to 255 in scanning interval of one. The CCD sensor works at 25.070.1 1C with exposure time of 0.20 s. (2) Flat-field calibration: When the planar light source enters an ordinary optical system, the vignetting could occur since the light flux has a decrease with the increasing off-axis angle.
4. Image processing Before analysis of performance, an image processing is carried out as shown in Fig. 3. The averaged dark noise image firstly needs to be obtained by averaging the 100 original dark images from step (3). This image is used to be subtracted by the original interferograms from step (1) and flat field images from step (2). The flat field calibration plays an important role in this optical system for analysis of performance. There are few factors that may
H. Gao et al. / Optics Communications 292 (2013) 36–41
39
Fig. 3. The image processing. All original images from the experiment need to be operated by this process to generate the qualified images for analysis of instrument performance. The flat-field calibration is an important step which can reduce adverse effects from the luminous flux variation with regard to the incident angle.
let a uniform planar source at object plane be an uneven image with dark edge through the system. This is mainly attributed to the decrease in the light flux with increasing incident angle. The changing reflectance of LCoS regarding to incident angle may be also a reason. Additionally, the tiny non-collimated optical system may cause the uneven distribution of the light intensities. Thus, in order to recover the standard flat field image, we carry out a consequent process by averaging the 50 original images from the flat field calibration testing, removing the noise, and smoothing by using a square array of 3 3 neighboring pixels. Reading out the gray levels of all pixels, and storing them in a matrix, the standard flat field image can be converted into the matrix form. Finding the max value of this matrix, and all the other values divided by this max value can give the flat-field coefficient matrix in which all the values are less than unit. Subsequently, all the original images derived from step (1) need to subtract the dark noise separately and are smoothed by using a square array of 3 3 neighboring pixels. Using the matrixes converted by these processed images to multiply the flat-field coefficient matrix mentioned above, we can finally obtain the qualified images for analysis of instrument performance.
5. Results and discussion 5.1. Phase modulation range and linearity Before the analysis, the fringe center in each processed image needs to be determined by calculating the extremum of a Gaussian fitting curve to the horizontal and vertical cross sections of the image. Sampling 20 images by an equal interval from one complete experiment, we ultimately identify an averaged center pixel number of (245, 260). Then the value by averaging the 25 neighboring pixels around the center pixel is calculated as the center value of one image. Fig. 4(b) shows the central values of all images drawn with regard to gray levels (or image serial numbers) as discrete dots for 532 nm. The solid line is the sine fitting curve for the discrete dots by least square means with adjusted R-square value of 0.948. The fitting curve is also a calibration for relationship between the gray level and the phase variation for analysis in next section. For the more convenient analysis,
Fig. 4. The phase modulation and linearity results. (a) The linearity and maximum range of phase modulation for 532 nm. (b) The sine calibration curve according to the relationship between gray values of LCoS and image for 532 nm. It indicates the maximum phase modulation of 6.699 rad (about 2.13p) and the modulation interval of 0.026 rad based on this 8-bit LCoS.
the fitting curve needs to be converted into a standard line by the linearization as shown in Fig. 4(a), and the deviations are drawn as discrete dots. This result indicates the maximum phase modulation of 6.699 rad (about 2.13p) and the modulation interval of 0.026 rad based on this 8-bit LCoS for 532 nm. Fig. 5 shows the same phase modulation information as Fig. 4 but with the wavelength of 633 nm. The solid line is also the sine fitting curve with adjusted R-square value of 0.978. From the perspective of the comparison, the result in Fig. 5(a) indicates that the maximum modulation of 4.951 rad (about 1.58p) for 633 nm is less than the value for 532 nm, so the modulation interval increases to 0.019 rad for each one gray level. This changing trend agrees with the description from the manufacturer. The data stability and linearity for 633 nm are slightly better than that for 532 nm. Since that the principle of ‘‘four-point algorithm’’ for wind measurement only requires the maximum modulation of 1.5p [17], the results in this section demonstrate the basic ability to cover this range if two significant airglow emission lines of OI (557.7 nm) and OI (630.0 nm) are employed. 5.2. OPD variation and instrument visibility In order to analyze the OPD variation with regard to the incident angle, we take one representative image to implement the calculation. For making full use of all the information of the whole image, the image is divided into several cycles with the width of one pixel from fringe center to edge. Based on the relations from the fitting curves of Figs. 4(b) and 5(b), the gray
40
H. Gao et al. / Optics Communications 292 (2013) 36–41
Fig. 6. The OPD variations with regard to incident angle. Green discrete spots and black solid line are experiment data and theoretical curve respectively for 532 nm. Red discrete spots and blue solid line are experiment data and theoretical curve respectively for 633 nm. (b) The instrument visibility variations with regard to incident angle for 532 nm (green spots) and 633 nm (red spots). For 532 nm the OPD variation at incident angle of 3.61 is 0.59 wavelengths, while the value for 633 nm is 0.50 wavelengths. The maximum difference of only 0.09 wavelengths between these two curves suggests the good achromatic ability. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The phase modulation and linearity results. (a) The linearity and maximum range of phase modulation for 633 nm. (b) The sine calibration curve according to the relationship between gray values of LCoS and image for 633 nm. It indicates the maximum phase modulation of 4.951 rad (about 1.58p) and the modulation interval of 0.019 rad based on this 8-bit LCoS.
level by averaging all pixels in each cycle can be corresponded to the phase shift from fringe center. Since each cycle has a linear relation to incident angle, the OPD variation with incident angle can be obtained by a conversion shown in Fig. 6. For 532 nm, the OPD variation at incident angle of 3.61 is 0.59 wavelengths, while the value for 633 nm is 0.50 wavelengths. The maximum difference of only 0.09 wavelengths between these two curves suggests the good achromatic ability. When the incident angle is less than 0.81, the instability of gray values appears in both curves. The random noise of CCD may be charged with the primary responsibility for this deviation due to the fewer pixels in the circle near the fringe center. The apparent visibility is a product of the emission line visibility and instrument visibility. The emission line visibility can be used for deriving temperature, since the spectral line broadening has a strong dependence of temperature. While, the apparent visibility has a significant impact on the signal-to-noise ratio (SNR) of the image, and it may also affect the accuracy for deriving wind. In this analysis, the spectral line visibility is considered as a known quantity because of the selected laser source, and the apparent visibility can be calculated by the fringe amplitude. Thus, we can obtain the instrument visibility from the apparent visibility divided by the spectral line visibility. With the same operation as shown in Figs. 4(b) and 5(b), 12 square bins of 5 5 pixels are sampled from center to edge in each image with an equal interval. Although the range of 0.226–0.191 for 532 nm is overall higher than that of 0.204–0.146 for 633 nm, as seen
Fig. 7. The instrument visibility variations with regard to incident angle. The instrument visibility variations with regard to incident angle for 532 nm (green spots) and 633 nm (red spots). The range of 0.226–0.191 for 532 nm is overall higher than that of 0.204–0.146 for 633 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from the results in Fig. 7, all the values are slightly lower than that are expected. At normal incidence the reflectivity of LCoS for 532 nm is only 62%, while the value of fixed mirror coated with silver is about 95%. The difference between two reflectivity values could impact on the light intensities from two arm of interferometer, and therefore reduce the instrument visibility by a factor of 10% at least. The reflectivity of 53% for 633 nm could make the visibility lower than that for 532 nm. The decreasing trend of visibility with regard to the increasing incident angle attributes to the same variation trend in the reflectivity of LCoS with incident angle. Furthermore, some other aspects, such as the wave front error of the manufactured optics and the polarization effects of the beam splitter and polarizers, could impact on the instrument visibility to some extent [19].
H. Gao et al. / Optics Communications 292 (2013) 36–41
5.3. Discussions From the results above, it seems obvious that the LCoS depends strongly on the wavelength. The shorter wavelength may prefer to provide modulation range with a higher value. While the decreasing wave front error with increasing wavelength may lead to more stability and consistency of data. This deduction has a consistency with the description in reference [20]. From a comprehensive view, however, the LCoS is more suitable for the wavelength of 557.7 nm emitted from O(1S) of airglow emission rather than for 630.0 nm from O(1D). As seen from Figs. 4(b) and 5(b), when the incident angle is in the range of 0.8–3.61, there are still small discrepancies. The fringe superposition of inevitable multiple reflections among the optical surfaces such as the polarizers and mirrors, and the wave front error making the fringe shape become nonsinusoidal, are considered as the main reasons, even though we have set the polarizers to be tilted by a small angle [19]. In addition, Figs. 4–6 show the phase fluctuations. The power instability of two lasers may be a partial reason. The main reason seems to be attributed to the electronic addressing of the liquid crystal by pulse modulation [21]. This weakness can be effectively reduced by the former analog LC-SLM technology to decrease the low frequency fluctuations [8], and by using polarizing state generators [20] or controlling temperature [22]. Although the application of LCoS in wide-angle MI can satisfy the basic requirements for wind measurement, it still has some inadequacies to be improved. The higher phase modulation accuracy requires more stability of the electrical components in LCoS. To increase the instrument visibility, reducing the reflectance of fixed mirror to the same level as LCoS may be a more effective method rather than increasing fill factor of LCoS. Since the LCoS works at polarized state, the light throughput has been weakened a lot before arriving at CCD sensor. Thus, if the very weak airglow emissions are employed as the targets, we must expand the effective area of LCoS in order to enhance the e´tendue and responsivity of the optical system. Also, only the sufficient large e´tendue makes it possible to simultaneously implement four phase steps as mentioned in reference [15]. While, this very potential method involves a complex separated imaging system and more technical challenges, and how to realize this concept has been determined as the focal research in our further work.
6. Conclusions In summary, we have proposed a wide-angle MI based on LCoS as a stepping device with no moving part to provide an effective technique for upper atmospheric wind measurement. The experiment are designed and operated to obtain a sequence of interferograms. By the image processing and analysis, the results indicate the maximum phase modulations of 2.13p for 532 nm and 1.58p for 633 nm can cover the necessary detection range.
41
The OPD variations with regard to incident angle for both wavelengths are within 0.59 wavelengths, while the instrument visibilities of 0.226–0.191 for 532 nm and 0.204–0.146 for 633 nm still need to be improved in the further work. The phase fluctuations are mainly attributed to the multiple reflections, the wave front error, the electronic addressing by pulse modulation and the power instability of the lasers. We also give the aspects for improving performance. Though, this novel device has been proved its effectiveness, and we hope that it can provide an innovative way for the research field.
Acknowledgments The authors would like to thank the support by the National Natural Science Foundation of China (Nos. 10874138, 41027004 and 61275185), the Education Office of Shaanxi Province (No. 09JK653), and the Excellent Doctoral Dissertation Fund of Xi’an University of Technology (No. 101-211104).
References [1] G. Shepherd, G. Thuillier, W. Gault, B. Solheim, C. Hersom, J. Alunni, et al., Journal of Geophysical Research 98 (1993) 10725. [2] G. Shepherd, G. Thuillier, Y. Cho, M. Duboin, W. Evans, W. Gault, et al., Reviews of Geophysics 50 (RG2007) (2012) 1. [3] J.C. Bird, F. Liang, B.H. Solheim, G.G. Shepherd, Measurement Science & Technology 6 (1995) 1368. [4] W. Gault, S. Sargoytchev, S. Brown, Proceedings of SPIE 4306 (2001) 266. [5] W.E. Ward, W.A. Gault, G.G. Shepherd, N. Rowlands, Proceedings of SPIE 4540 (2001) 100. [6] C. Englert, D. Babcock, J.M. Harlander, Applied Optics 46 (2007) 7297. [7] J. Harlander, C. Englert, D. Babcock, F.L. Roesler, Optics Express 18 (2010) 26430. [8] N. Collings, T. Davey, J. Christmas, D. Chu, B. Crossland., Journal of Display Technology 7 (2011) 112. [9] S.T. Wu, D.K. Yang, Reflective Liquid Crystal Displays, John Wiley & Sons Inc., Chichester, 2005. [10] H. Dai, K. Xu, Y. Liu, X. Wang, J. Liu, Optics Communications 238 (2004) 269. [11] Z. Cao, Q. Mu, L. Hu, D. Li, Z. Peng, Y. Liu, et al., Optics Express 17 (2009) 2530. [12] D. Sinefeld, D. Marom, Optics Letters 37 (2012) 1. [13] W. Osten, C. Kohler, J. Liesener, Journal of Optics A: Pure and Applied Optics 38 (2005) 71. [14] F. Bai, F. Han, Y. Xu, X. Bao, S. Gan, Optics and Lasers in Engineering 49 (2011) 932. [15] H. Gao, Y. Tang, D. Hua, L. Qin, C. Zhu, Journal of Quantitative Spectroscopy & Radiative Transfer 112 (2011) 268. [16] H. Gao, Y. Tang, D. Hua, H. Liu, Applied Optics 50 (2011) 5655. [17] G. Shepherd, W. Gault, D. Miller, Z. Pasturczyk, S. Johnston, P. Kosteniuk, et al., Applied Optics 24 (1985) 1571. [18] G. Shepherd, Spectral Imaging of the Atmosphere, Academic Press, New York, 2003, pp. 133–134, pp. 146–147, pp. 175–180. [19] W.E. Ward, Z. Pasturczyk, W.A. Gault, G.G. Shepherd, Applied Optics 24 (1985) 1589. [20] A. Lizana, A. Ma´rquez, I. Moreno, C. Iemmi, J. Campos, M. Yzuel, Journal of the European Optical Society—Rapid Publications 3 (2008) 08011. [21] J. Moore, N. Collings, W. Crossland, A. Davey, M. Evans, A. Jeziorska, et al., IEEE Photonics Technology Letters 20 (2008) 60. [22] J. Garcı´a-Ma´rquez, V. Lo´pez, A. Gonza´lez-Vega, E. Noe´, Optics Express 20 (2012) 8431.