Mikrochim. Acta [Wien] 1987, III, 309--324

Mikrochimica Acta 9 by Springer-Verlag1988

Fourier Transform Spectroscopy Using Image Sensors Shigeo Minami Department of Applied Physics, Faculty of Engineering, Osaka University, Yamada-oka, Suita 565, Japan

Abstract. Multichannel Fourier transform spectrometers utilizing image sensing devices are reviewed along with the instrumental design concepts. Although the idea itself is fairly simple, a photographic plate in holographic spectroscopy is replaced by an image sensor, there are stringent requirements to be satisfied in order to realize the system for field use. Mainly two types of the instrument, which are characterized by the Sagnac common-path interferometer and the polarization interferometer optics, respectively, are described with regard to their system performances. Examples of the system operation introduced show that Fourier transform spectrometers without mechanical moving parts play an important role in a variety of spectroscopic applications under severe surroundings. In a summary, methods for the resolution enhancement and comments on the signal-to-noise ratio are also included. Key words: Fourier transform spectroscopy, interferometer, image sensor, multichannel Fourier transform spectrometer.

The widespread use of Fourier transform spectroscopy (FTS) in chemistry has been drastically changing the spectroscopic techniques especially in the IR region. Undoubtedly, this trend was pushed by the advancement of computer technology which made a multi-point Fourier transform computation available with a limited amount of cost and time. This is a typical example of reviving an old innovation as a modern tool through the achievements in the high-tech era. The ideas and experimental trials concerning FTS [1--3] by many reputed scientists were practically realized by virtue of contemporary technology. One example that has recently come up in one of the branches of the FTS instrumentation stream is a multichannel FTS method which will be presented here. In connection with the computer technology, the recent progress of multichannel photoelectric sensors plays an important role in this method. It is well known that image tubes were often adopted in spec-

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troscopic measurements to replace photographic plates since television had become popular. This technique is still used today when a variety of sensitive image sensors are commercially available. Thus, multichannel optical spectrum analyzers are widely spread because of their multichannel advantage as well as their mechanical simplicity. Needless to say that the replacement of a photographic plate by an image sensor achieves a more sensitive and reliable spectroscopic measurement over the ordinary spectrograph or mechanically scanning spectrometer under the same optical throughput. In this context, one may recollect the holographic spectroscopy demonstrated by Stroke and Funkhouser in 1965 [4]. They clearly demonstrated that an incoherent Fourier transform hologram irradiated by a coherent beam in Fourier transform optical arrangement reconstructs a spectrum of the source. In fact, the hologram itself is a two-beam interference pattern on the photographic plate, and the reconstruction process is nothing but the optical Fourier transform in analog fashion. During the last decade in which holographic spectroscopy has been used, numerous approaches were carried out [5--9]. However, nobody tried to replace the photographic plate by an image tube and to utilize a digital computer for reconstructing the spectrum through numerical Fourier transformation. It seems strange that no one tried to use imaging devices with holographic spectroscopy; this could be understood by considering the following limitations: (1) most of the commercially available image tubes only cover the UV-visible region, (2) the dynamic range of the image tube was not wide enough to accept the white-light interference pattern, (3) the advance of accurate scanning mechanisms made the conventional FTS instrument commercially acceptable. Because of the above-cited reason and due to the increase of popularity of commercially available instruments especially in chemistry, holographic spectroscopy faded away after the early 1970's. Almost at the same time, solid-state image sensors appeared on the market, and have since been used as optoelectronic sensors of compact spectrometer in multichannel fashion. Recently, the solid-state image sensor has become an indispensable element for a small spectrometer which fulfills the requirements of field use. This current trend including the daily revision of the image sensor characteristics was enough to remind spectroscopists of the variety of the holographic spectroscopy techniques that utilizes photographic plates. The first paper on multichannel Fourier transform spectrometer (MCFTS) combining the holographic spectroscopic technique and a linear photodiode array was published by the Osaka University group in 1984 [10]. Since then the MCFTS has been attracting the interest of spectroscopists who are looking for something new. Even though many problems remain unsolved, the MCFTS which inherently includes no mechanical moving parts has the feasibility of realizing a rugged spectroscopic sensor for a variety of field applications, and offering a high-speed, time-resolving operation as well.

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Basic System Structure Just as a conventional FTS instrument, the MCFTS system is divided into two subsystems, a two-beam interferometer optics and a data manipulation electronics. Fig. 1 illustrates the system principle in comparison with the holographic technique. The photographic plate is replaced by the image sensor to avoid interfering the real-time operation by the wet process.

Interferometer Optics Most of the interferometer configurations used in holographic spectroscopy are applicable. The necessary requirements imposed onto the interferometer optics specifically for field use are as follows: (1) (2) (3) (4) (5) (6)

Special consideration for white-light fringe formation. High contrast fringe formation. High optical throughput. Easy adjustment and stable operation. Vibration-free robust construction. Small size.

In order to fulfill the above requirements, two-beam interferometers generating either equal inclination or equal thickness fringes are adopted. However, it isrecommended to select the optical configuration in which two interfering beams travel through the approximately common path including the minimum number of optical elements. For instance, a Michelson type interferometer is not useful according to the above-

Interference fringes (Hologram)

=~

COHERENT RADIATION H?Iogram

Spectrum

FEROMETER OPTICS

PHOTO-PLATEA A %'WETPROCESS, ' ~

FOURIER OPTICS (ANALOG FT)

PHOTO-PLATEB

[HOLOGRAPHIC SPECTROSCOPY] Interference fringes SOURCE

INTER-

O ~

FEROMETER

/ Spectrum ACQUISITION INTERFACE

( A
oPrTCS IMAGE SENSOR

NUMERICALFT (FFT)

[MCFTS USINGAN IMAGESENSOR] Fig. 1. System principle of the MCFTS illustrated in comparison with holographic spectroscopy

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mentioned requirements. The optical throughput is gained by the field of view and the entrance lens size, however, the aberration and vignetting should be taken into account. The aberration of optics affects not only the fringe visibility but also the sampling accuracy. Although the MCFTS does not aim at a high spectral resolution, a trade-off between the aberration and the spectral resolution under the limited throughput is rather critical. In addition, the limited height of the photodiode array also raises a similar problem.

Image Sensor and Data Manipulation Electronics A spatially spread interference fringe pattern is received by an image sensor, such as a linear photodiode array, an area array, and an image tube. These image sensors have to be of a charge integration type which includes photoelectric transducer, charge storage, and charge transfer sections in one device. Since these devices have the limited dynamic range from 50 to 60 dB, the exposure time which is generally determined by the scanning rate should be carefully selected under consideration of the central fringe intensity. Before digitally processing the interference fringe pattern, the pattern has to be sampled and digitized. The mode of the sampling operation substantially depends upon the sensor employed. The solid-state linear or area array sensor in which the pixel elements of the same size are accurately aligned generates a sampled signal evenly spaced, whereas the image tube output being sampled with an external circuit includes a considerable sampling error mainly due to the aberration of the electron optics. In any event, since the MCSTF inherently has limited resolution, it is preferable to compute a power spectrum from a double-sided interferogram (a component of the interference fringe pattern). The rest of the problems to be considered using the image sensor concerns the locality of the sensitivity. This causes a slow spurious background of the interferogram. Fortunately, this background commonly has very low frequency components in most cases, and it belongs to a category of systematic errors which can be compensated by some ways. In the MCFTS, the subtraction technique uses either an anti-phase interferogram or a pure background level intentionally introduced by destroying the interference condition. The numerical processing of the digitized interferogram consists of pre-, main-, and post-processing. The main processing is the digital Fourier transformation by means of the FFT algorithm. The total number of cell elements in the image sensor for the MCFTS is as large as 1024, so that the computation by conventional personal computers is practically acceptable. The necessary time to generate the spectrum is one second on the average by using a program written in machine language. Needless to say that up-to-date FFT digital signal processors drastically reduce the computation time. As far as Fourier transform processing is concerned, there might be no problem in the MCFTS technique. In preprocessing, the data gathering with ensemble averaging and smoothing are common procedures for enhancing the signal-to-noise ratio.

Fourier Transform Spectroscopy Using Image Sensors

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Commercially available solid-state image sensors could be operated with a very high clock rate of about 10 MHz; however, the optimum data rate should be carefully determined after considering the central fringe intensity and dynamic range of the sensor, as well as the maximum acceptable data rate of a data acquisition system. Even though a high speed A-D converter is implemented, the operation time for computer inputting restricts the total speed. In the case of high-speed time-resolved spectroscopy, it is recommended to use a digital wave memory which includes an ultra-fast converter and several data buffer areas to accommodate successive interference patterns. Such high-speed buffers are also useful for the data averaging procedure with slow computers. A variety of postprocessing procedures are becoming important in spectroscopy. Numerical data processing for enhancing the spectral resolution is sometimes necessary for MCFTS data because of its limited resolution. One can enjoy deconvolution and AR (autoregressive) model fitting methods with inexpensive personal computers nowadays. A typical data manipulation system composed of a microcomputer integrated buffer interface and a personal computer is shown in Fig. 2. The exposure time and the interval between effective scanning operations can independently be set by computer commands. A 12 bit-8~s A-D converter is used, therefore a minimum exposure time of 10 ms, which corresponds to each scanning time, can be allowed for a 1024 channel linear array. This system or a partly modified one was commonly used in the MCFTS described in the following. MCFTS Using a Triangle Common-Path Interferometer

The Sagnac common-path interferometer is one of the suitable optical arrangements which satisfies the requirements for the MCFTS optics. The triangular configuration using two mirrors was recommended in holographic spectroscopy [5] to produce straight high-visibility fringes. After the MCFTS using the triangle optical configuration was introduced, the MCFTS with the Sagnac three mirror interferometer has reported [11]. It utilizes the equal thickness interference fringes, and the system is also characterized by the clever background compensation technique. Here, a MCFTS with triangle common-path interferometer will be described [10]. Fig. 3 shows an optical arrangement of the system. The beam

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sl .:,:

t

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D

from source S is divided into two by beam splitter BS. Each of the two beams travels the same triangular path formed by two mirrors M1 and M2 in the opposite direction and is recombined by BS. The recombined beams are focused by lens L on its back focal plane where a linear photodiode array sensor is placed. Under the perfectly symmetric set-up in which mirror M1 is placed at the position indicated by the dashed line, no interference fringes are observed on the sensor plane. If M1 is shifted by a toward the direction of the source S with keeping the surface exactly in parallel, the straight fringes of equal inclination appear. This optical adjustment leads to the splitting of the virtual image of the source shown in the figure. The distance 1 between the two virtual sources becomes l/2 a, extended virtual sources have an equal spacing 1. This is a principle of source-doubling interferometers in which the equal inclination interference fringes are generated with any extended incoherent source. The principle itself is eventually equivalent to Fourier transform optics which is characterized by its shiftinvariant nature. In this arrangement, the fringe intensity I as a function of the spatial distance x becomes co

I(x) = I g(00)B(o-)(1 + cos2:rc001x/f)d00, (1) 0 where B(o-) is the spectrum of the source, K(00) is the system characteristic function, 00 is the wave number, and f i s the focal length of lens L. In this arrangement, the theoretical spectral resolution 60~and the maximum wave number 00maxare given by 600 = f / d . 1. N, (2) O'max

=

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(3)

F o u r i e r Transform Spectroscopy Using Image Sensors

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where d is the pitch of the sensor cell elements and N i s the total number of the elements. 8o-and O'maxcan be changed with 1which is settled by the pulllength of M1. In any situation, the theoretical resolving power R is always equal to one half of the total number of the cell elements N. In practical implementation of the interferometer optics, a beam splitter cube of 40 x 40 x 40 mm was used with two flat mirrors, M1 and M 2 , of 60 mm in diameter. As lens L, an achromatic telescope lens of 450 mm focal length and 60 mm in diameter was utilized. A self-scanning photodiode linear array was employed as an image sensor. The Matsushita MN8090 employed comprises 1024 elements, each of which size is 464 #m long and 16 r wide, and the pitch of the periodic array structure is 28 #m. Since each element size has an aspect ratio approximately 3 0 : 1 for multichannel dispersion spectrometers, it also gives a significant benefit for the measurement of vertical fringes. Its spectral coverage is from 300 to 1200 nm on the average. The system performance was examined by observing a He-Ne laser and a low pressure mercury lamp. Fig. 4 presents an interferogram-spectrum pair for the He-Ne laser output. The laser beam was expanded to 20mm in diameter and led to the system after passing through a vibrating scatter plate for eliminating the speckle pattern. The background of the interferogram is considerably distorted at both ends mainly due to the vignetting. The interferogram was obtained by single scan with an exposure time of 213 ms. The computed &r and O-maxwere 56 and 29 000 cm-1, respectively. An interesting behavior of the system is demonstrated in Fig. 5. This figure shows how the mercury spectrum pattern behaves as mirror M1 is He-Ne LASER

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Fig. 5. Successive change of the reconstructed mercury spectrum Corresponding to the displacement of mirror M1. Relationships between the pull-length a and related spectral parameters are tabulated in the lower part of the figure

successively displaced. As presented in Eqs. (2) and (3), 60-and O'max are becoming smaller when the pull-length a is getting larger. Spectra E and F in the figure clearly show the folding of the spectrum due to an aliasing effect. In these situations, the sampling theory is not valid any more for accurately accommodating the fine structure of the interference fringes.

Fourier Transform Spectroscopy Using Image Sensors

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MCFTS Using a Polarization Interferometer

The previously described MCFTS utilizing the triangle common-path interferometer which generates the equal inclination interference fringes has many attractive features; however, there exists a spatial restriction if a small spectroscopic sensor is used for field applications. The following description is on a MCFTS utilizing birefringent interferometer which is capable of realizing a compact optical configuration [12]. In contrast to the preceding system, the interferometer here produces the straight equal thickness interference fringes. In order to avoid the degradation of the fringe visibility, the source area should be limited. The optical throughput is gained by the large acceptance angle rather than the source area. A variety of polarization interferometers have been developed and certain types have already been applied to the conventional FTS instruments in conjunction with the scanning mechanism [13, 14]. Recently, the polarization interferometer was also adopted to holographic spectroscopy [151. Fig. 6 shows an optical layout of the MCFTS employing a polarization interferometer. The interferometer based on the birefringent interference can make it possible to align all elements in-line and to lead the two interfering beams in approximately the same path. Such an optical configuration satisfies the requirements for the stable and rugged interferometer optics. In the figure, the beam from the radiation source is collimated and linearly polarized by polarizer 1. This component is divided into two orthogonally polarized beams with a separating angle 0 by a three-element Wollaston prism. The two polarized beams are recombined by polarizer 2 and generate an interference fringe pattern, which is localized at a plane inside the Wollaston prism. A combination of an imaging lens and an auxiliary cylindrical lens makes a spatially distributed fringe pattern on an image sensor. 0

SOURCE CONDENSER LENS APERTURE

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SEPARATING ANGLE = 3,44 ~ APERTURE i0 xlOmm

POLARIZER 2 IMAGING LENS CYLINDRICAL LENS PHOTODIODE ARRAY

MAGNIFICATION M=I4

MN8090

Fig. 6. Typical layout of the optics using a polarization interferometer

318

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The fringe intensity as a function of the spatial axis x is presented by the following equation which is similar to Eq. (1), oo

I ( x ) = f K ( c r ) B ( c r ) (1 + cos 2 ~ c r O x / M ) d a , o

(4)

where 0 is the separating angle of two polarized beams, and M is the lateral magnification factor. Accordingly, the resolution ~cr and the maximum wave number a~,x are calculated by ~cr = M / O . d . N

(5)

and cr,,ax = M / 2 0 "

d = N " c~cr/2.

(6)

Needless to say that N / 2 equals the theoretical resolution. Two types of MCFTS were constructed for the UV-visible and for the near IR region by utilizing the same principle. In the former, the threeelement Wollaston prism employed is made of quartz crystals. The aperture and the separating angle are 10 • 10 mm wide and 3.44 ~ at 546.1 nm, respectively. The interferogram localized inside the prism is magnified by a factor of M -- 14 and projected onto the image sensor. The source radiation is collimated by the lens of 55 mm focal length after being focused on the entrance aperture of 4 mm in diameter. The latter system is a modification of the former for accommodating the near-IR radiation [16]. All the optical elements were replaced by near-IR elements as well as by the image sensor. The interferometer optics is composed of two fused quartz lenses of 50 mm in diameter and 120 mm focal length, a two-element Wollaston prism of 30 x 30 mm aperture and an average separating angle of 20 rain, and two Polaroid-HR for the near-IR. To temporarily realize a near-IR MCFTS under the limited expense, an IR vidicon (Hamamatsu, N214-06) was used as the image sensor. Such TV imaging devices are not suitable to achieve a good performance because of their non-linearity and small dynamic range in intensity measurement. Furthermore, a considerable amount of image distortion cannot be neglected. As an associated electronics for gathering the interference pattern data, a commercially available frame memory is usable, although the exposure time is restricted by the video scan rate. The wavelength range is mainly limited by the spectral characteristics of the polarizer elements and the IR vidicon, which ranges only from 0.7 to 2.2 #m. In the MCFTS using the polarization interferometer, the following two points should be noted. The first one is the influence of the refractive index dependence of the Wollaston prism on the wave number. The separating angle 0 of the polarized two beams which passed through the Wollaston prism depends on the wave number, Since the relationship between wave number a and discrete sampling point k in the spectrum is given by k = N. d.cr.

O(cr)/M,

(7)

a wave number calibration procedure is necessary to present the reconstructed spectrum on a linear wave number scale.

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The second part is an advantage of easy compensation for the background superimposed on the interferogram. This is due to the optical set-up in which an anti-phase interference pattern can readily be obtained by rotating the analyzing polarizer at an angle of 90 ~. By subtracting the antiphase interference pattern from the in-phase one, an enhanced interferogram without background can be provided. Some of the performance data given by the measurement of simple spectra will be presented. Fig. 7 is the interferogram and the reconstructed spectrum for a Cd lamp obtained by the UV-visible MCFTS. The measurement of a He-Ne laser radiation was also carried out under a similar arrangement as that for the previous example, and spectral resolution &r and maximum wave number O-maxwere confirmed as 70 cm- 1 and 36 000 cm-1, respectively. The interferogram and the reconstructed spectrum provided by the near-IR MCFTS using the vidicon is presented in Fig. 8 for a diode laser which emits 1.3 # m radiation. Since the interference pattern totally covering the effective surface area of the vidicon was collected, the interferogram was considerably distorted and eventually apodized. Nevertheless, it was gamma corrected and then transformed. The result roughly shows that the spectral resolution in the near-IR region is approximately 100 cm- 1.

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Examples of Its Application Some results obtained by the MCFTS in practical measurements will be briefly demonstrated.

Time Resolved Spectroscopy A cadmium hollow cathode lamp for atomic absorption spectroscopy was lit at ordinary working conditions and the current was slowly cut off. The emission was observed by the MCFTS using the triangle common-path optics. Fig. 9 shows the time-resolved spectra of the emission involving Cd and Ne lines. Both the resolution time and the exposure time were kept 10 ms.

Microspectrofluorimetry A polarization MCFTS was combined with an universal optical microscope by Hitachi Co. group [17]. A plant leaf was irradiated by 390 nm of a semimonochromatic source and a fluorescence emission from a spot of 5 #m in diameter is received by the MCFTS. The interferogram and the reconstructed spectrum are shown in Fig. 10. In the spectrum, a chlorophyl fluo-

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Near IR Diffuse Reflectance Spectroscopy The near IR MCFTS was applied to diffuse reflectance spectroscopy for examining food-stuffs [18]. Two spectra which respectively correspond to regular and moist flour are shown in Fig. 11. The lower wave number sides of these spectra are unfortunately cut by the limited spectral response of the IR vidicon. It is clear that a slight extension of the region toward the lower wave number might make this instrument more useful as a tool in food industry.

Summary Fourier transform spectroscopy using image sensors were reviewed along with certain design considerations. The description rather focused on the MCFTS which were developed by the author's laboratory. The original idea came from the combination of holographic spectroscopy and image sensor technology. Accordingly, a variety of achievements accumulated in the research on holographic spectroscopy was modified in the developing process of the MCFTS. Since the MCFTS chiefly aims at the field spectroscopic sensor, the pertinent choice of robust and stable interferometer optics is one of the essential aspects. Although high spectral resolution is not expected in the MCFTS, several approaches were carried out for enhancing the resolution. These procedures could not be described in this review; however, they were mentioned briefly. As already pointed out, the resolving power R is theoretically determined by the total number of the sensor cell elements. The use of large image sensors restricts the reduction of the size of optics; on the other

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hand an increase of the cell density leads to its sensitivity deterioration in addition to its severe consequence for the optical accuracy. To cope with these situations, optical or mathematical methods were tried. In the optical method, heterodyning techniques which were used for high resolution holographic spectroscopy [19, 20] are also applicable to the MCFTS. In practice, this method is realized by placing a dispersive optical element in the interferometer optics in order to give the angular dispersion to two interfering beams. Modifications of this idea were successfully utilized for MCFTS to enhance the resolution significantly [21, 22]. Another way is the use of a mathematical treatment. Basically, this method is based on the estimation of the spectrum from data of finite length. In Fourier transform spectroscopy, it is equivalent to extrapolating a finite length interferogram to that of a longer length including the region in which no interferogram measurement is done. A variety of mathematical methods already developed [23] are applicable in the MCFTS. The AR model was applied to the MCFTS and it was seen that a resolution enhancement of more than several times is attainable. [24, 25]. However, the mathematical methods include a lot of pitfalls. They are not always recommendable for taking reliable spectra. Lastly, the signal-to-noise ratio of the MCFTS is to be considered. The theoretical treatment is rather complicated because the sensor parameters and characteristics which include the dynamic range and the noise behavior are still ambiguous. Furthermore, it is difficult to estimate an RL product (resolving power times luminosity) because of the spatial matching problems between the interference pattern and the image sensor, even though the MCFTS theoretically has a large optical throughput. In the present state, the actual performance of the MCFTS is comparable with that of the multichannel dispersive spectrometer with similar resolution. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

P. Connes, Infrared Phys. 1984, 24, 69. P. B. Fellgett, Infrared Phys. 1984, 24, 95. H. A. Gebbie, Infrared Phys. 1984, 24, 105. G. W. Stroke, A. T. Funkhouser, Phys. Lett. 1965, 16, 272. K. Yoshihara, A. Kitade, Jpn. J. AppL Phys. 1967, 6, 116. K. Kamiya, L. Yoshihara, L. Okada, Jpn. J. AppL Phys. 1968, 7, 1129. S. Lowenthal, C. Froehly, J. Serres, C. R. Acad. Sci. Paris 1969, 168B, 1481. K. Yoshihara, L. Nakashima, M. Higuchi, Jpn. J. Appl. Phys. 1976, 15, 1169. H. J. Caulfield, Holographic Spectroscopy (Advances in Holography, Vol. 2), (N. Farhat, ed.), Marcel Dekker, New York, 1976, p. 139. T. Okamoto, S. Kawata, S. Minami, AppL Opt. 1984, 23, 269. T. H. Barnes, AppL Opt. 1985, 24, 3702. T. Okamoto, S. Kawata, S. Minami, AppL Spectrosc. 1986, 40, 691. W. M. Sinton, J. Quant. Spectrosc. Radiant. Transfer 1963, 3, 551. L. Mertz, Transformation in Optics, Wiley, New York, 1965, p. 53. H. Barnils, J. M. Simon, Optik 1984, 68, 209. S. Minami, T. Okamoto, S. Kawata, Proc. SPIE 1985, 553, 346. S. Matsui, W. Matsuo, I. Nemoto, H. Hirose, Tokyo Conf. for Appl. Spectrosc. Tech. Digest, The Japan Soc. Anal. Chem., Tokyo, 1987, p. 173.

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[18] S. Kawata, Y. Inoue, K. Sasaki, S. Minami, Tokyo ConfforAppl. Spectrosc. Tech. Digest, The Japan Soc. Anal. Chem., Tokyo, 1987, p. 42. [19] T. Dohi, T. Suzuki, Appl. Opt. 1971, 10, 1137. [20] F. Lanzl, B. Reuter, W. Waidelich, Opt. Commun. 1972, 5, 354. [21] T. Okamoto, S. Kawata, S. Minami, Appl. Opt. 1985, 24, 4221. [22] T. H. Barnes, T. Eiju, K. Matsuda, Appl. Opt. 1986, 25, 1864. [23] Special issue on spectral estimation, Proc. IEEE 1982, 70, No. 9. [24] S. Kawata, K. Minami, S. Minami, Appl. Opt. 1983, 22, 3593. [25] K. Minami, S. Kawata, S. Minami, AppL Opt. 1985, 24, 162.

Received August 24, 1987.