Compact Liquid-Crystal-Polymer Fourier-Transform Spectrometer

Compact liquid-crystal-polymer Fourier-transform spectrometer Gerben Boer, Patrick Ruffieux, Toralf Scharf, Peter Seitz, and Rene´ Da¨ndliker

We present the optical design and realization of a low-resolution liquid-crystal 共LC兲 Fourier-transform spectrometer 共FTS兲. This FTS is based on a polarization interferometer that has a Wollaston prism made of a LC material as a key component. It has a compact design, a good acceptance angle, and low temperature dependence and can be fabricated with cost-effective LC technology. Because the LC is polymerized, it is robust, and the temperature dependence is drastically reduced. The performance of a compact handheld version of the spectrometer and the characteristics 共angular dependence, resolution, stray light, and temperature dependence兲 will be discussed. © 2004 Optical Society of America OCIS codes: 120.6200, 160.3710, 120.3180, 230.5440, 160.5470.

1. Introduction

In comparison with other types of spectrometer, such as grating spectrometers or Fabry–Perot resonators, the Fourier-transform spectrometer 共FTS兲 has wellknown throughput and multiplex advantages.1,2 The multiplex advantage exists only if the system is detector noise limited, and it is particularly significant for measurements in the mid-infrared and far infrared. In the near-infrared and visible ranges, shot-noise-limited imaging is more likely to occur, and in this case there is no fundamental multiplex advantage 共Fellgett兲 over grating devices, although the throughput 共Jacquinot兲 advantage is retained. Another advantage is that the spectral range that is covered by the FTS is limited only by the sensor sensitivity and absorption of the elements that constitute the spectrometer. The actual commercially available FTSs are mainly used for application in the When this research was performed, G. Boer 共gerben.boer@ epfl.ch兲 was with Centre Suisse d’Electronique et Microtechnique SA Zu¨rich, Badenerstrasse 569, 8048 Zu¨rich, Switzerland. He is now with Sciences et Techniques de l’Inge´nieur兾Institute ´ cole Polytechnique Fe´de´rale de d’Imagerie d’Optique Applique´e, E Lausanne, CP 127, 1015 Lausanne, Switzerland. P. Seitz is with Centre Suisse d’Electronique et Microtechnique SA Zu¨rich, Badenerstrasse 569, 8048 Zu¨rich, Switzerland. P. Ruffieux, T. Scharf, and R. Da¨ndliker are with the Institute of Microtechnology Neuchaˆtel, University of Neuchaˆtel, Rue A.-L. Breguet 2, 2000 Neuchaˆtel, Switzerland. Received 18 June 2003; revised manuscript received 14 January 2004; accepted 22 January 2004. 0003-6935兾04兾112201-08$15.00兾0 © 2004 Optical Society of America

near- and far-infrared regions for chemical analysis or astronomical observations. They contain very precise moving parts and are, consequently, large, expensive, and fragile and can be used only in protected environments. So, they are obviously not suited for applications needing compact and robust spectrometers, such as portable devices. Grating spectrometers are mostly used for such applications. The aim of the present paper is to fabricate a spectrometer that overcomes the drawbacks of the common FTS and keeps, to the extent possible, the benefits of it. For this purpose, we need a compact monolithic FTS that can be fabricated with low-cost technologies. For achieving this goal, one approach is to miniaturize a static Michelson interferometer with a tilted mirror as presented by Manzardo et al.3 Another approach by Manzardo et al.4 is the fabrication of a time-scanning Michelson interferometer by using silicon micromachining technology. A similar approach is presented by Collins et al.,5 in which a 10-cm-large scanning Michelson has been microfabricated. A different, interesting system is a static FTS based on a polarization interferometer using a Wollaston prism as a phase shifter. These spectrometers are generally realized with a Wollaston prism made of conventional inorganic crystals6 –15 共mostly calcite兲. The same spectrometers can be realized with liquid-crystal 共LC兲 materials,16 which make them more affordable and offer new design possibilities, by use of, for example, twisted LC structures.17–19 However, as we will see in the present paper, the temperature dependence of the LC birefringence is a major problem for industrial appli10 April 2004 兾 Vol. 43, No. 11 兾 APPLIED OPTICS

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will see later兲, is recorded by the photodetector array 共PDA兲. 5. Finally, a numerical Fourier transformation of the spatial intensity distribution gives the spectral intensity. The measured intensity 共interference兲 pattern Iout recorded by the PDA is given by integration over all wave-number components; hence I out共r兲 ⫽ Fig. 1. Principle of a FTS based on a Wollaston prism.

兰

␴

1 B共␴兲 D共␴兲T共␴兲 K兵1 ⫹ 兩␮ 12共r, ␴兲兩 4

⫻ cos关␦共 y, ␴兲兴其d␴, cations. To overcome this drawback, we developed a spectrometer that uses LC-polymer technology. Here the LC that is generally in the liquid phase is solidified by UV polymerization. This has the advantage to make the spectrometer more robust and less temperature dependent. 2. Principle

The core of the spectrometer consists of a birefringent system made of two wedge-shaped LC cells, a twisted nematic cell 共TN cell兲, two polarizers, and a switchable TN cell. The use of the switchable TN cell will be explained later. Figure 1 shows schematically the FTS with its principle operation explained below. 1. The natural incoming light is linearly polarized at 45° with a dichroic sheet polarizer. 2. The light is decomposed into two linear polarization components x and y by the first prism. Owing to the birefringence and the geometry of the prism, it produces a spatially varying phase shift in the y direction between the two polarization components 共in the x and y directions兲. After the first prism, the polarization components are rotated by 90° when traversing the TN cell. The total phase shift at the output of the birefringent system is given by ␦ ⫽ 4␲␴关n e共␴兲 ⫺ n o共␴兲兴tan共␪兲 y ⫹ ␦ TN,

(1)

where ␴ ⫽ 1兾␭ is the wave number with ␭ as the wavelength of the light, ␪ is the prism angle, y is the position along the detector array, and no共␴兲 and ne共␴兲 are the ordinary and the extraordinary refractive indices of the LC material, respectively. ␦TN is a constant phase shift that is produced by the TN cell. This constant phase shift is relatively small in that the TN cell is only 20 ␮m thick compared with the wedges’ thickness of 200 ␮m. At the center, when y ⫽ 0, the phase shift produced by the first prism is compensated for by the second prism, and the relative phase shift is ␦TN. 3. The two polarization components are recombined by the second polarizer 共or analyzer兲, which is oriented at ⫾45° to obtain maximal contrast. 4. The interference pattern, which is localized just at the exit of the modified Wollaston prism 共as we 2202

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(2)

where ␮12共r, ␴兲 is the spatial coherence20 between the two polarization components, ␦共 y, ␴兲 is the phase shift given by Eq. 共1兲, T共␴兲 is the transmittance of the optical system, D共␴兲 is the spectral sensitivity of the detector, K is the fill factor of pixels of the detector, and B共␴兲 is the spectral distribution of the irradiance of the unpolarized incident light. The above formula does not take into account possible contrast reduction due to scattering or to not ideal polarizers. It also assumes that the spectrometer has no defects 共phase distortions兲 and infinite length 共no truncation兲. The spatial coherence depends generally on the position r of observation and the numerical aperture 共NA兲 of the system. For a perfectly spatial coherent source 共such as a laser兲, ␮12 will be unity independently of r. In this case the contrast of the interference fringes defined locally by 共Imax ⫺ Imin兲兾共Imax ⫹ Imin兲 will be maximum. In the case of a spatially incoherent source, ␮12 will be smaller than 1. But there exists a plane for which ␮12 and, consequently, the contrast of the fringes can be maximal. In this paper we will call this plane the plane of maximal contrast. The spectral distribution of the irradiance B⬘ as seen by the spectrometer is given by the Fourier transform of the intensity distribution of Eq. 共2兲; hence B⬘共␴兲 ⫽ FT兵I共␦兲其 ⫽

兰

␦max

I out共␦兲cos共␦ ⫹ ⌬␦兲d␦,

(3)

⫺␦max

where ⌬␦ is a phase-correction term that is introduced to compensate for eventual nonlinear phase distortions caused by the birefringent elements of the spectrometer. This phase correction will be discussed in more detail later in this paper. The true spectrum of the incoming light source can be retrieved by one’s dividing B⬘共␴兲 by a white measured reference spectrum 共containing the information about D, T, and K兲. Experimentally, we obtain the output intensity as a function of the position y and not as a function of ␦ as indicated in the above formulas. In this case, the spectral intensity is given in spatial frequencies. The spectral distribution as a function of the wavelength can be retrieved with the help of a calibration table that relates the spatial frequency of the interferogram to the wave number ␴ of the light.

3. Optical Design

There are many possible configurations combining different wedges and TN cells that can produce the necessary phase shift for the FTS. We have chosen the configuration of Fig. 1 mainly for three reasons. 1. Because it uses only two LC wedge cells 共which are the most difficult to fabricate兲, it is a relatively simple and compact configuration. 2. As already shown in a previous study,18 it has a low angular dependence 共large field of view, NA ⬎ 0.35兲 compared with other configurations 共at least for small optical path differences兲. 3. The optical axis of the wedge cells needs only small tilt angles 共respective to the entrance and exit faces兲 to project the plane of maximal contrast out of the system. In a simple Wollaston prism 共when using a spatially incoherent source兲, the interference fringes 共or plane of maximal contrast兲 are localized within the system. When the optical axis of the first prism is tilted adequately, the plane of maximal contrast can be projected out of the system.21 This last point is crucial because conventional LC technology allows only a limited tilt angle of the optical axis of approximately 7°–10° when rubbed polyimide is used as an alignment layer. If this plane of maximal contrast is situated inside the system, additional optics are needed to image the interferogram on the PDA. This would, of course, make the system bulky and complicated to build. We compared theoretically and experimentally the localization of the plane of maximal contrast of the three different configurations. A. Classical modified Wollaston 共or Normarski兲 prism with the optical axis of the first prism tilted by an angle ␣. B. Two wedges with oppositely tilted axes and a TN cell in between 共as shown in Fig. 1兲. C. Optical axes of the wedges are oriented by ⫾45° with respect to the horizontal plane and have opposite tilts. The polarizers are here oriented horizontally and vertically. The maximal tilt angle ␣, which is given by technology constraints, is the same for all three configurations and is set to be ␣ ⬇ 7°. For simulations, we used T ⫽ 230 ␮m, a wedge angle ␾ ⫽ 0.6°, and ⌬n ⫽ 0.19 共no ⫽ 1.51 and ne ⫽ 1.71兲, which corresponds approximately to the parameters of the fabricated systems. We also included the glass substrates of the cells in the model that are approximately 0.5 mm thick. To determine theoretically the localization of the plane of maximal contrast, we simulated the three configurations described above with the nonsequential commercial ray-trace program ASAP.22 To be able to deal with the twisted structures present in the design, we used a ray-trace method23 that divides the TN cells into a set of homogenous uniaxial layers

Fig. 2. Interferograms simulated with a nonsequential raytracing program for different localizations of the detection plane behind the exit surface.

with their optical axes slightly rotated with respect to each other. The localization of the plane of maximal contrast has been found by our illuminating the system with a monochromatic spatially incoherent source and by placing the detector iteratively at different locations. The location for which the observed fringes have maximal contrast corresponds to the plane of interest. Figure 2 shows simulations for configuration C at three different positions of the detection plane. These simulations show that the plane of maximal contrast is situated at 1.5 mm behind the exit surface of the spectrometer. For configuration A, one finds 1.0 mm and, for B, 2.4 mm. We have obtained the experimental values by placing the LC spectrometers in a polarization microscope and by directly observing the localization of the fringes. To have a sharp localization of the fringes 共␮12 decreasing rapidly in the z direction兲, we illuminated the spectrometer with a high aperture 共NA approximately 0.6兲. We determined the location by measuring the distance between the position where the objective is focalized on the exit surface of the spectrometer and the position where the maximal fringe contrast is observed. The measured values are, for configuration A, 1.2 ⫾ 0.2 mm and, for B, 2.2 ⫾ 0.2 mm. Configuration C has not been fabricated. The most sensitive parameter is the pretilt angle 共or the tilt angle of the optical axis兲. A variation of 1° can shift the localization of the fringes by a few hundred micrometers. In that we could estimate the pretilt angle of the fabricated cells only within a precision of ⫾1°, the slight discrepancy is understandable. These results show that the position of maximal contrast of the interference fringes varies strongly with the chosen configuration. Practically, we are interested in having a maximum space available behind the exit face for placing the PDA housing 共1.5 mm兲 and the sheet polarizer 共⬃0.3 mm thick兲. In principle, the higher the tilt angles, the further the plane of maximal contrast is localized from the exit face. But because the tilt angle is limited by the technology, we have to choose the configuration that for a fixed tilt angle gives the furthest position of the plane of maximal contrast. For this reason, we finally have chosen configuration B 共shown in Fig. 1兲. 4. Realization of the Spectrometer

We obtained the wedge-shaped and the twisted planar cells by placing foil spacers between two 25 mm ⫻ 10 April 2004 兾 Vol. 43, No. 11 兾 APPLIED OPTICS

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Fig. 3. 共a兲 Handheld FTS prototype. 共b兲 Birefringent part of the spectrometer with polarizers compared with a 2 Swiss franc coin.

25 mm glass substrates, 0.55 mm thick, partially sealed with UV glue 共Norland兲. The substrates were covered with a rubbed high-pretilt polyimide 共Nissan, SE-610兲 layer to produce the high-pretilt alignment of the LC molecules. This alignment process permits us to obtain a tilt of the optical axis of approximately 7°. For the twist cell the two substrates were rubbed in perpendicular directions. The cells were filled by capillarity with a polymerizable LC-silicone mixture from Wacker 共⌬n ⫽ 0.19兲 containing also 1‰ photoinitiator 共Irgacure 907, Ciba兲. Because of the high viscosity of this LC at room temperature, the cells were filled at 110 °C and were kept 30 min in the nematic phase at 110 °C to permit the LC to align uniformly. When all the domain walls had disappeared, the cell was cooled down to room temperature while the LC stayed in the nematic phase. To avoid mechanical and stress birefringence, it is recommended to cool down the cell very slowly 共typical cooling rate ⬃3 K兾min兲. Finally, the LC is cross linked at room temperature with UV A light 共⬃10 mW兾cm2兲. The polymerization process should be slow enough to avoid unwanted distortions. The switchable planar TN cell,24 which is placed just after the first polarizer, has a thickness of 23 ␮m and is filled with a conventional LC mixture 共ZLI1132 from Merck兲. Its optical axis is oriented at 45° 共parallel to the axis of the first polarizer兲. To rotate the entrance polarization by 90°, it is switched by a 30-V 共rms兲 alternating voltage 共20-kHz兲 power supply. The PDA is 512-pixel complementary-metal-oxidesemiconductor linear image sensor from Hamamatsu 共Model S5463-512Q兲. The pixels have a width of 19 ␮m and a height of 500 ␮m, and the pitch is 25 ␮m. This detector is chosen mainly for its large pixels and its high saturation, achieving a high signal-to-noise ratio. The readout electronics has a 14-bit analogto-digital converter and a Universal Serial Bus communication interface. To demonstrate the miniaturization possibilities and the robustness of such a spectrometer, we built a handheld version designed for colorimetry.25 Figure 3共a兲 shows the external aspect of the prototype. The upper cubic part of the prototype contains the modified Wollaston prism with the polarizers shown in Fig. 3共b兲 and the PDA. The lower cylindrical part 2204

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Fig. 4. Deformation of a wedge-shaped cell. The thickness variation can be transposed into a shift of the interferogram in the y direction.

contains an illumination system26 that permits one to illuminate samples under standard conditions. It consists of a circular LED array and a concentric inclined mirror. To perform and evaluate 共Fourier transform, phase correction, etc.兲 the measurements, we connect the spectrometer to an acquisition module and a computer. Notice that the measurements presented in the experimental section were not performed with this apparatus but with a well-defined optical setup to obtain a more accurate characterization. The performances of this prototype are similar to that ones we present here and are mainly limited by the illumination module. 5. Correction Methods

The LC-polymer elements are not perfect. However, some errors produced by defects of the birefringent elements can be corrected. We present here two correction methods. The first method, which has already been used for a Michelson interferometer,27 allows one to correct for geometrical deformations of the wedges and takes phase nonlinearities into account. The second method28 reduces the static noise produced by local defects. Fabrication errors such as thickness variations or stress birefringence cause undesired phase distortions. We have noticed experimentally that the phase distortion is due only to deformations of the birefringent elements and is not caused by local variations of the birefringence. As shown in Fig. 4 for a simple birefringent wedge, the thickness variation ⌬T in the z direction can be translated into a shift ⌬y in the y direction. This is valid for slowly varying phase distortions. In this case the phase error ⌬␦共 y兲 can be written as ⌬␦共 y兲 ⫽

2␲ ⌬y共 y兲⌬n共␭兲tan ␾. ␭

(4)

We can find the distortion of the interferogram ⌬y共 y兲 by comparing the measured pattern with the ideal interferogram produced by a monochromatic light source. The ideal interferogram gives a perfect sinusoidal signal with equidistant zeros. The measured interferogram shows some deviations from this perfect signal. The shifts ⌬y共 y兲 for the zero points of the interferogram can be deduced from the difference between the ideal zero positions and the real zero

positions. Because the thickness variation of the wedges is relatively smooth, we can find the other points of ⌬y共 y兲 by fitting the measured points with a polynomial function. The corrected spectrum can then be retrieved by our introducing ⌬␦共 y兲 into the Fourier transform as was done in Eq. 共3兲. Because we assume that the phase distortion is caused only by thickness variations, this correction is wavelength independent, and we can apply the same correction ⌬y to all wavelengths. The measured interferograms present a fix-pattern noise due to contamination of the LC material or dust particles. This noise that is imposed on the real signal S can be 共in approximation兲 decomposed in an additional part included here in the bias P and a multiplicative part described by the factor m. The recorded interferogram has the form I ⫽ 共S ⫹ P兲共1 ⫹ m兲. To attenuate the fix-pattern noise we apply a method already used by Hashimoto and Kawata.29 In this method, a first 共in-phase兲 interferogram I1 is recorded where the polarizer and analyzer are oriented perpendicular to each other. Then a second 共antiphase兲 interferogram I2 is recorded where the polarizer and the analyzer are parallel. The subtraction of these two interferograms 共I1 and I2兲 is performed, the bias 共mean intensity兲 P is suppressed, and the signal S of the interference pattern is doubled. If we assume that the factor m is independent of the intensity and the bias is constant, the subtraction of the phase and antiphase interferograms can be written as I ⫽ I1 ⫺ I2 ⫽ 共S ⫹ P兲共1 ⫹ m兲 ⫺ 共⫺S ⫹ P兲共1 ⫹ m兲 ⫽ 2共S ⫹ mS兲.

(5)

Finally we end up with an interferogram in which the bias and the fix-pattern noise on the bias are removed and the signal S is twice as high. However, the multiplicative part of the noise on the signal remains. Instead of rotating the polarizer mechanically, we introduce as a switchable polarization rotator a TN LC cell in the setup as shown in Fig. 1. A properly designed cell rotates the entrance polarization by 90° when it is in the off state 共no electric field, V ⫽ 0兲 and does not affect the entrance polarization when it is in the on state 共V ⫽ 0兲. The TN cell must be aligned so that its optical axis given by the nematic alignment direction is parallel or perpendicular to the polarization direction of the polarizer. 6. Experimental Results

The following experimental results were obtained by use of a LC-polymer spectrometer as described in Fig. 1 and a spatially incoherent source. No additional optics were used to image the interferogram on the detector. To produce a homogenous spatially incoherent light source, we used a light guide. Light from a xenon lamp and a He–Ne laser was used for illumination and coupled in the light guide. At the output of the light guide, we placed a moving diffus-

Fig. 5. 共a兲 Phase correction applied to each pixel of the interferogram. The maximum accumulated phase deviation is approximately half the fringe period. 共b兲 Uncorrected 共dashed curve兲 and phase-corrected spectra 共solid curve兲 for monochromatic light of 570 nm.

ing plate with diameter of 5 cm. At a distance of 20 cm, we placed our spectrometer. A circular diaphragm between the diffusing plate and the spectrometer sets the aperture of the system. To avoid nonlinear distortions due to saturation or a low-light detector-noise-limited regime, we regulated the optical power of the source so that the photodetector worked approximately in the middle of its working range. Interferograms were obtained with a singleshot measurement and two shots for the phase– antiphase correction. The integration time was 160 ms, and the NA of the system was 0.35 共⫾20°兲. The vignetting produced by the diaphragm naturally apodizes the interferogram. No mathematical apodization has been performed. The effect of the phase correction is particularly spectacular when it is applied to narrowband spectra. Figure 5共a兲 shows the phase-correction function ⌬␦ obtained by comparing the ideal spectrum with the 10 April 2004 兾 Vol. 43, No. 11 兾 APPLIED OPTICS

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Fig. 6. Spectra obtained by illuminating the spectrometer with a He–Ne laser. Stray-light suppression is significantly increased by use of the phase–antiphase correction.

measured spectrum of a He–Ne laser. We applied this phase correction to a measurement obtained by coupling monochromatic light at 570 nm in the light guide and by limiting the illumination with the diaphragm to NA ⫽ 0.1. The dashed curve of Fig. 5共b兲

shows the uncorrected spectrum, and the solid curve represents the spectrum obtained from the same interferogram but corrected with the method described above. Similar results were obtained for different wavelengths. These measurements show clearly that geometrical deformations of the birefringent elements can be corrected. The fix-pattern correction described in Section 5 is useful to reduce the noise produced by local defects. Figure 6 shows the measured spectrum of a He–Ne laser in logarithmic representation. Both measurements with and without fix-pattern noise correction were made with exactly the same setup described above and with NA ⫽ 0.35. The measurement obtained with the fix-pattern noise-correction method shows significantly less noise than the one without correction. At 50 nm from the center of the peak, we obtain a stray-light suppression of approximately 22 dB in the optical domain. The theoretical resolution of the spectrometer ⌬␭ ⫽ ␭2兾共T⌬n兲 gives 8 nm for ␭ ⫽ 570 nm, ⌬n ⫽ 0.19, and T ⫽ 230 ␮m. The FWHM of the corrected peak of Fig. 5 is approximately 10 nm. This discrepancy is due to the natural apodization produced by the vignetting of the optical system that reduces the resolution. In addition, the PDA does not completely cover the whole Wollaston prism, therefore diminish-

Fig. 7. Measurements of a edge filter cutting at 495 nm. 共a兲 In-phase interferogram, 共b兲 antiphase interferogram, 共c兲 difference between 共a兲 and 共b兲, and 共d兲 normalized Fourier transform of 共c兲, which represents the transmission curve of the filter. The windows show magnified parts of the interferograms. 2206

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spectrum that has exactly the shape of the transmission function of the filter. The abnormal intensity rise between 400 and 430 nm reveals a very low signal-to-noise ratio, and we can consider here that the cutoff wavelength is at approximately 420 nm. This is due to the poor transmission of the spectrometer in this region as we will see in Section 7. 7. Throughput

Fig. 8. Transmission curve of the complete spectrometer including the polarizers and TN cells.

Fig. 9. Temperature dependence of prototypes with a conventional LC and with a LC polymer. The curves indicate the shift rate measured with monochromatic light sources 共500 and 650 nm兲 at different temperatures.

ing slightly the effective value of T. A second measurement shown in Fig. 7 has been obtained by our placing a sharp-edge filter that cuts all the wavelengths below 495 nm without affecting the wavelength above 共GG495 from Schott兲 in white-light illumination 共xenon lamp兲. Figures 7共a兲 and 7共b兲 show the in-phase and antiphase interferograms. The interferogram of Fig. 7共c兲 demonstrates how the bias and the fix-pattern noise 共visible in the magnified areas兲 can be attenuated by subtracting the interferograms shown in Figs. 7共a兲 and 7共b兲. The spectrum of Fig. 7共d兲 is the Fourier transform of the interferogram of Fig. 7共c兲 divided by the spectrum obtained when the edge filter 共spectrum of the xenon lamp兲 is removed. So we obtained a normalized

To get high signal-to-noise ratios and short measurement times, it is important to have a high throughput and a good overall transmission. The total transmission of our spectrometer is mainly given by the two polarizers and the absorption of the prisms. Ideally, if we consider natural incoming light, the first polarizer absorbs 50% of the light, and the second polarizer absorbs again 50% of the remaining light. That results in a total transmission of 25%, assuming that all the other elements are perfectly transparent. But the birefringent elements also absorb as much as 30% of the incoming light. So, we may expect a total transmission of approximately 18%. We measured the transmission of the complete system 共prisms and polarizer兲 with a Perkin– Elmer spectrometer as shown in Fig. 8. Because we used an integration sphere, the forward-scattered light is also included in the measurements. As we see, the transmission decreases drastically below 450 nm. This is due not only to the poor transmission of the LC elements and their scattering losses but also to the absorption of the sheet polarizer in this spectral region. Notice that for larger wavelengths the transmission is always higher than the maximal value of 25%. This is due to the imperfect extinction ratio of the polarizers. For better performance, new LC materials that absorb less in the blue region have to be found. 8. Temperature Dependence

One critical point in the use of LCs in spectrometer applications is their temperature dependence. We investigated this experimentally for two prototypes: a first one made of a conventional LC mixture 共ZLI-1132兲 and a second one made of photocrosslinkable LC polymer 共silicone-type material from Wacker兲. The designs of the two spectrometers are almost identical. To measure the temperature dependence, we put the prototypes into a temperature-controlled test chamber 共Vo¨ tsch VT4004兲. The spectrometer was illuminated with monochromatic light 共spectral width of ⌬␭ ⬇ 5

Table 1. Overview of the Key Parameters and Performances of the Investigated Spectrometer Shown in Fig. 7

Characteristic

Quantity

Size Resolution Field of view Stray-light suppression Average transmission 共visible兲 Cutoff wavelength Temperature dependence

25 mm ⫻ 25 mm ⫻ 6 mm 共without detector兲 10 mm 共at 570 nm兲 ⬎35° 共depending on optical path difference兲 ⬍20 dB 共for ␭ ⬎ 420 nm兲 ⬃18% 420 nm 0.1 nm兾K 10 April 2004 兾 Vol. 43, No. 11 兾 APPLIED OPTICS

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nm兲 via a waveguide. We recorded the localization of the measured spectral peak every 5 K. The results, which are summarized in Fig. 9, show that the wavelength shift at room temperature can be reduced from 1 nm兾K for conventional LC mixtures24 to a more acceptable rate of 0.1 nm兾K for LC polymers. We have also observed that even lower temperature dependence, down to 0.03 nm兾K, can be obtained by using a postpolymerization process. 9. Summary

We have shown that it is possible to fabricate a lowresolution FTS by using polymer LC technology. The spectrometer was made compact, and the angular dependence was reduced by our choosing a specific prism configuration. The plane of maximal contrast can be projected out of the system sufficiently to put the PDA directly behind the exit face of the birefringent prisms. No additional imaging optics was needed. Eventual geometrical deformations due to the fabrication process of the birefringent wedges can be corrected with a simple calibration measurement that has to be performed only once. Static noise produced by local defects can be considerably reduced by one’s performing a phase–antiphase measurement with the help of a switchable TN cell. The main characteristics of this spectrometer are listed in Table 1. Compared with a FTS made out of inorganic materials, the main advantage of the polymer LC version presented in this paper is the use of a cost-effective LC technology, which would permit mass production. But there are also drawbacks, such as poor transmission of the used materials below 450 nm and the modest resolution of the spectrometer limited by the maximum thickness that can be achieved with LC technologies. However, we think that, with new LC materials that have better transmission in the visible range, the actual spectrometer would then become an interesting alternative to grating spectrometers, for example, in the field of colorimetry. We thank the Consortium fu¨ r Chemische Industie and Wacker Chemie GmbH for their collaboration and the supply of the LC-polymer materials. The research was partially founded by the Commission for Technology and Innovation and the Albert Ko¨ chlin Stiftung. References and Notes 1. R. J. Bell, Introductory Fourier Transform Spectroscopy 共Academic, New York, 1972兲. 2. J. Chamberlin, The Principle of Interferometric Spectroscopy 共Wiley Interscience, Chichester, UK, 1979兲. 3. O. Manzardo, P. Kipfer, and H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” in Fourier Transform Spectroscopy: New Methodes and Applications 共Optical Society of America, Washington, D.C., 1999兲, pp. 165– 167. 4. O. Manzardo, H. P. Herzig, C. R. Marxer, and N. F. de Rooij, “Miniaturized time-scanning Fourier transform spectrometer based on silicon technology,” Opt. Lett. 24, 1705–1707 共1999兲. 5. S. D. Collins, R. L. Smith, C. Gonza´ lez, K. P. Stewart, J. G. Hagopian, and J. M. Sirota, “Fourier-transform optical microsystems,” Opt. Lett. 24, 844 – 846 共1999兲. 2208

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