Multi Channel Array Interferometer-Fourier Spectrometer

Multi Channel Array Interferometer-Fourier Spectrometer A. Manuilskiy, H.A. Andersson, G. Thungström, H-E. Nilsson

matrix detector. This allows a compact integrated device with reduced complexity to be built. This leads to an increase in its reliability and in its ability to function under severe climatic conditions and mechanical disturbances. In addition it also offers a reduction in the production costs. The main principle of this multi-channel Fourier transform spectrometer (MCFTS) is that the interference pattern created by it under certain conditions is localized to a position very close to the interferometer and can be measured by an array or matrix detector. A Fourier transform of such an intensity distribution provides the spectra of incident light. Ideas concerning the uses of the interference pattern of reflected light from thin films to achieve the spectral content of light have been known for some time [2]. A development of these ideas to the design of devices using these principles for the transmitted light was recently done [3]. The practical realization of these principles meets some problems such as that involved in the manufacturing of very thin interferometers whose minimum thickness is significantly less than that of the shortest measured wavelength etc. Attaching the interferometer to the detector, thus causing a minor gap to occur between them, can also prove to be problematic. However, even the case where the

 Abstract— The characterization and design of a Fourier transform spectrometer, which enables the integration of a multi channel interferometer with a detector unit in order to create a compact device is presented in this paper. It operates within a wide spectral range from visible to NIR, contains no moving parts and is resistible to mechanical and climatic conditions. Such a design with an array or matrix detector can be used for spectroscopy with a partially coherent or white optical source depending on the shape of the optical interferometer. A reasonable spectral resolution of the order of 20-50 cm-1 can be achieved over a 1 μm wavelength range when using a 512 pixel detector array. A design model for characterization of the quasi integrated device, where a multi channel interferometer was mechanically attached and which contained a gap to the detector elements, was used. The experimental results are promising and suggest a variety of different directions for the development and application of these types of integrated spectrometers.

Index Terms—Fabry-Perot interferometers, spectroscopy, Optical spectroscopy, Spectroscopy

Fourier

I. INTRODUCTION The current trend is development of low cost and high reliability spectrometers for industries and other applications with a reasonable resolution requirement, a few nm. Traditional Fourier transform (FT) spectrometers based on Michelson interferometers consist of an optical interferometer, detector or array detector and intermediate optics [1]. The latter creates an interference pattern on the detector surface. The optics produce a significant impact on the whole design of the spectrometer and do not enable a compact device to be built. An FT Spectrometer can be built by attaching a multi channel Fabry-Perot interferometer directly to an array or Manuscript received June 26, 2006. A. Manuilskiy is with the Mid Sweden University, Department of Information Technology and Media, Sundsvall, Sweden (e-mail: [email protected]). H. A. Andersson is with the Mid Sweden University, Department of Information Technology and Media, Sundsvall, Sweden (Phone: 046 60 148717; fax: 046 60 148456; e-mail: [email protected]). G. Thungström is with the Mid Sweden University, Department of Information Technology and Media, Sundsvall, Sweden (e-mail: Goran [email protected]). H-E. Nilsson is with the Mid Sweden University, Department of Information Technology and Media, Sundsvall, Sweden (e-mail: Hans-Erik [email protected]).

1-4244-0435-5/06/$20.00 ©2006 IEEE.

Fig. 1. Optical layout of the integrated multi channel Fourier spectrometers with stepped (a), wedge (b), and cylindrically (c) shaped interferometers. S – Optical source, L – Collimated optics, I-1, I-2, I-3 – Interferometers, D-1,D-2 – Array detectors with different sized pixels, R – Read out electronics, 4 Angle of incidence of light, C – Reflection coating, G – Gap between interferometer and detector,

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I

- Wedge angle.

design of the multi channel interferometer does not have a thickness value close to zero and is not attached very closely to the detector array, can have interesting applications. A design model for the characterization of the quasi integrated device where a multi channel interferometer, including a gap, is mechanically attached to the detector elements was used. The experimental results have been promising and offer a variety of different directions for the development of such kinds of integrated spectrometers.

intensity of the interference pattern provides the spectra of the incident light. Increasing R causes the appearance of second and higher harmonics of the spectra. It can be seen from (3) that for non coherent light sources, the maximum energy of the interference pattern is concentrated where the light passes the interferometers with the smallest thickness and that this section of the interferometer is important for the analysis of this type of light. The thicker part of the interferometer is important for the analysis of light with higher coherency. For a correct spectrum reconstruction the interferometer array should contain individual interferometers whose thicknesses range from zero to a given maximum and where the incremental steps for the optical thickness are less than half that of the shortest wavelength in the incident radiation. In principal, it is possible for steps whose optical thickness exceeds the proposed limit to be used in the case where additional restrictions have been included. A wedged shaped interferometer can be used instead of a stepped shaped if the wedge angle, I , is so small that the period of the interference pattern for the shortest wavelength of interest is at least twice that of the distance between the array pixels, see Fig. 1b. For a small reflection coefficient, R, a wedge shaped interferometer produces interference patterns similar to those created by two beams inclined at a small angle, 2 M . However according to the optical layout of the MCFTS it is not possible to achieve a phase shift between interfering beams from negative – passing through zero – to positive values and these are those in general use in standard FT spectrometers with Michelson interferometers. The latter produces a two sided

II. THEORETICAL BACKGROUND According to the main principle of the multi channel FT spectrometer and whose optical layout is displayed in Fig. 1a, the light, whose spectral content is to be measured, passes the multi channel interferometer and is detected by an array detector attached directly to the interferometer. Spectral Response for an array of Fabry-Perot interferometers with variable thicknesses for the optical pass can be expressed by 1  R 2 (1) hX ,k 2 1  R 2  4 R ª«sin§¨ 2SQWk n 2  n1 ˜ sin 4 2 ·¸º» ¹¼ ¬ © where R – intensity reflectance of each interferometer surface, Q - frequency of incident light, n - refraction index of the space surrounding the interferometer, n1 - refraction index of the interferometer material, 4 - inclination of incident light and Wk - thickness of interferometer with number k (1...kmax), where kmax is determined by the highest resolution and can be defined as Wk W0  ( k  1)Md (2) where W0 - minimal thickness of interferometer, d – distance between interferometer pixels, M - coefficient of thickness change. The intensity of the spectra of the light transmitted by each interferometer is modulated periodically with a spacing equal to c / 2 ˜ Wk ˜ n1 , where c is the speed of light in vacuum if the angle of incidence, 4 is small and n1 1 . The spacing is inversely proportional to the optical thickness of the interferometers. It is apparent from (1) that when R is small the modulation of spectral response is based on an even harmonic function of the optical thickness of the interferometers. If the spectral content of the incident light is defined by the function gQ then the transmittance of the array of interferometers creates an interference pattern of light intensity behind the array interferometer, which can be defined as

,k

hQ ¦ Q

,k

gQ (3) Fig. 2. Spectrum of incident light containing non coherent and weak coherent component, (a), and corresponding interferogram intensity vs. number of pixels (solid line) and window function (dotted line), (b).

The localization of the interference pattern coincides with the interferometer surface if the diffraction effects for the optical layout are not significant, the interferometer is sufficiently thin and the angles of incidence are close to zero. The FT of the

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interferogram for the spectrum reconstruction. If the phase changes from zero, it can be used so called Fourier cosine expansion, [4], for even functions to construct a two sided interferogram from a one sided. In practice it is difficult to achieve initial zero phase difference when using a wedge interferometer because of manufacturing limitations. As a result some wedge interferometers, hereafter called "restricted wedges", produce an interferogram which lacks information with regards to small phase shifts. The influence of the residual minimal phase shift, when the spectrum is reconstructed, can be treated as an FT of the windowed interferogram. As mentioned previously the missing information for small phase shifts should lead to the suppression of spectral components with low coherency. Parseval´s relation can be used to estimate the level of the suppression of these components. To perform spectral changes, it is preferable to use the FT of the product of the functions representing the window and intensity of the interferogram. For partially coherent and coherent light it is clear that using a restricted wedge, which thus leads to information of small phase shifts being missing, is not so important for the reconstruction of the spectra. The simulation of the response of a spectrometer with a restricted wedge interferometer was performed using incident light containing a mixture of partially coherent and weak coherent light with a Gaussian spectra of width 100 nm and 1 nm respectively. The spectrum of the incident light is shown in Fig. 2a. In this case the wedge interferometer produces the one side interferogram shown in Fig. 2b (solid line), which was used for the reconstruction of the spectra of the incident light. In the case where the window is applied to the interferogram, as shown in Fig. 2b by the dotted line, then the resulting MCFTS spectrum is the convolution of the window function and the incident light spectra and is shown in Fig. 3. It can be seen that the ratio of the intensities for the obtained response for coherent and partially coherent radiation are of the order of 40dB. Such selectivity of the response of the spectrometer with a restricted wedge interferometer can be explained if the difference between the phase structure of the Fourier spectra for the window function, which is centered and then shifted from the center of the interference pattern in Fig. 4, is taken into account.

Fig. 4. The difference between amplitude and phase structure of the Fourier spectra of the window function centered and shifted from the center of the interference pattern.

The phase oscillations with amplitude r S

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of the shifted

window spectra results in a resulting amplitude which is decreasing when a convolution of the spectrum of non or partially coherent radiation and the spectrum of the shifted window function is performed. As a result of the previously mentioned suppression, it is not suitable to use the wedge shaped interferometer in order to achieve the spectra of non coherent sources. Improved results can be expected for spectrometers with cylindrically shaped interferometers attached to the detector, see Fig. 1c. In this case the minimal phase shift produced by such an interferometer can be much smaller. An approximate restoration of the spectrum for the case in which a small part of the interferogram is missing can be performed. By assuming that the alternative and normalized amplitude of the output from the array detector is placed behind the interferometer, with a missing part illuminated by monochromatic radiation and with a frequency Q then it can be represented by 2 AQ ,k cos¨§ 4SQ W0  (k  1)Md n 2  n1 ˜ sin4  2) 0 ¸· (4) © ¹ where ) 0 - the phase shift of incident light reflected from interferometer mirror may be considered to be constant. For the correct reconstruction of the spectra, it is necessary to calculate and assign the intensity of the interferogram corresponding to the point where the phase shift is equal to zero. For k = 1, which corresponds to the interferometer with minimal thickness, the expression (4) can be presented as AQ

Fig. 3. Resulting spectrum achieved by MCFTS with restricted wedge is the convolution of the window function and the incident light spectra.

cos4SQW0 ˜ cos2) 0  sin 4SQW0 ˜ sin 2) 0 (5)

Parameters W0 and ) 0 can be found for a given setup if signal AQ

for two different frequencies

Q1

and

Q2

is

measured. In this case, the approximate amplitude of the

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interferogram at zero phase shift can be assigned, for example, by spline approximation and a comprehensive interferogram can be constructed.

III. EXPERIMENTAL RESULTS The setup for the characterization of the types of integrated spectrometers previously described, consisted of both a wedge shaped and a cylindrically shaped interferometer with air gaps between the interferometer mirrors. These layouts are shown in Fig. 5. It can be more effective to use interferometer material with a higher refractive index, such as Si, as it requires no additional coating of the surfaces. Interferometer mirrors with suitable reflections and transmissions were made using glass plates and cylindrically shaped glass coated with 150Å Si layer to produce a wedge shaped air gap interferometer. The measured reflectance of the Si coated mirrors is shown for a wide spectral range in Fig. 6. The mirrors were coated with an Si layer as it is much more resistant to wear when in mechanical contact than for example Al. This is particularly important for the cylindrically shaped interferometer as mechanical contact takes place in a region of minimal thickness, which is important for the reconstruction of non coherent spectra. For the wedge interferometer with angle 2 mrad and length 50mm, the interferometer mirrors were separated from one side by a washer made from a 100 μm thick Si wafer and squeezed by a clamp in such a way that the opposite side of the mirrors had a very small gap, see Fig. 5a. The quality of the interferometer, which depends on the linearity of the changing thickness of the air gap, was checked by obtaining Fourier spectra of 630 nm and 1560 nm laser sources. The cylindrical interferometer with an air gap was assembled by squeezing a cylindrically shaped mirror of 100 cm radius onto a flat mirror, in such a way that the colour of the transmitted light from a white source was white for the middle of the interference pattern.

Fig. 6. Measured reflectance for Si coated mirrors for a wide spectral range.

The gap was also checked by taking interferograms from partially coherent optical sources with different wavelengths. A typical interferogram for the radiation of an LED source is shown in Fig. 7. These interferometers were attached to different types of arrays and matrix detectors in order to assemble the spectrometers. The detectors used were a Xenics 256 pixel extended InGaAs array working up to 2.5 μm, a Hamamatsu 1024 pixel Si array and a 320x240 pixel standard Si matrix detector. Different light sources were used to characterize the spectrometers such as laser and LED sources, and a Tungsten-Halogen lamp. For the laser sources no optics were used between the laser and wedge interferometer but for experiments with non coherent radiation, optics collecting light from a reflectance standard were used. Fig. 8a shows the spectra obtained simultaneously from a 630 and a 1560 nm laser source. Fig. 8b shows the spectra of a 630 nm laser and a 940nm LED source obtained simultaneously. In Fig. 9 the radiation spectra of 880 nm and 950 nm LED sources are shown and the reflectance spectrum of a broadband reflection standard from Labsphere (SRS-99-010) illuminated by a Tungsten-Halogen lamp achieved using a cylindrically shaped interferometer.

IV. DISCUSSION In accordance with the plot for reflectance, shown in Fig. 6, the spectrometers could operate over a wide spectral range from

Fig. 7. Typical interferogram for radiation of a LED source achieved with 640x480 pixels matrix array.

Fig. 5. Wedge shaped,(a), and cylindrically shaped,(b), model interferometers with air gaps between interferometer mirrors.

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Fig. 10. Normalized response of spectrometer vs. mirror reflectance of interferometer.

vs. pixel nr follows a quadratic law and in order to achieve a Fourier spectrum the spatial coordinates of the interference pattern were also scaled to a quadratic format. The spline approximation was also applied to the transformed interference pattern before Fourier processing. The profile of the transformed interferogram is shown in Fig. 11. It should be noted that, when using a cylindrical interferometer and a detector array with equally spaced pixels, it is impossible to achieve the maximum spectral resolution corresponding to the number of detector elements, because of the quadratic function of the phase shift from the centre of the interference pattern. Experimental results as shown in Fig. 9 are in good agreement to the expected results for the setup used.

Fig. 8. Spectra obtained from a 630 nm and a 1560 nm laser source simultaneously, (a) and spectra of a 630 nm laser and a 940 nm LED source obtained simultaneously, (b).

450 nm up to 2400 nm. The optimal reflectance for the wedge Fabry-Perot interferometer is approximately 34% and this is close to experimentally achieved results utilising these mirrors, see Fig. 10 and Fig. 6. Spectra of the lasers taken by processing the interference pattern (one-sided interferogram) created by the wedge interferometer attached to the XEVA linear array detector is shown in Fig. 8a. A broad spectral range from 630 nm to 1600 nm was achieved. No additional optics between the source and interferometer were used in this experiment. It was also possible to obtain spectra of LED and laser sources operating simultaneously when the LED source was placed at a distance of approximately 1000 mm from the spectrometer, see Fig. 8b. When achieving spectra for low coherency sources, the cylindrically shaped interferometer was used and the interference pattern created on the back surface of the interferometer was projected onto the array or matrix detector. By this way a spectra of LED sources in a range of 450-600 nm was also obtained. This approach was adopted because the minimum distance at which the interferometer could be attached, for example for the Xenics detector, was approximately 4mm and only a very low spectral resolution could be achieved in the case where the interferometer is attached to the window of the detector It is important to note that when using cylindrical interferometers the pass difference

V.

CONCLUSION

The concept of the Multi Channel Array InterferometerFourier Spectrometer is experimentally confirmed to work for a wide spectral range. A spectrometer with a restricted wedge interferometer is useful for applications that deal with partially coherent and coherent sources such as LED and lasers. The spectrometer with a restricted wedge interferometer exhibits strong suppression of the response for radiation sources with low coherency. For optical sources with low coherency it is effective to use a cylindrically shaped wedge interferometer because a minimal pass difference for Fabry-Perot interferometer can be achieved.

Fig. 11. The profile of the interferogram transformed by spline approximation. Fig. 9. Radiation spectra of 880 nm and 950 nm LED sources and reflectance spectrum of a broadband reflection standard illuminated by a TungstenHalogen lamp achieved with cylindrically shaped interferometer.

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