Laboratory model of static Fourier spectrometer

The optical design of FS is shown in Fig.1, where S - light source, C - collimator, M1, M2 - plane mirrors, B - beam splitting cube, L - lens, CCD - cooled 512x1 elements linear CCD array, I - interface, including control logic CCD, amplifier, 10-bit ADC and buffer for connection with computer.

Fig.1. Fourier spectrometer system block diagram.

The mirrors M1, M2 and beam splitter B forms Michelson interferometer with tilted mirrors. CCD array detects interference pattern in the focal plane of lens L. The beam splitter has possibility be moved in M2 direction for interferometer alignment.

Measured optical spectra of Ne-discharge lamp, Hg-arc lamp and tungsten lamp are shown in Fig.2 (a)-(c) respectively. As one can see the spectral resolution is unsatisfactory for atmosphere investigation. This fact connected with low frequency response of CCD array due to small format of it. Obviously to correct this problem we must use CCD array of larger format of about 2000. On the other hand we must take into account the spatial frequency response of CCD array that reduces registration of high spatial frequencies.

Fig.2 Interference pattern and its FFT of different light source: (a) Ne-discharge lamp, (b) Hg-arc lamp, (c) tungsten lamp, (d) He-Ne laser.

To obtain the response function of our FS model we use the He-Ne laser as light source. In Fig.2 (d) one can see the common output FS interference pattern and FS response function. In our model spectral resolution (R = n/Dn ) was of about 60 and was restricted mainly by small format of CCD array.

To improve the spectral resolution R of FS model we have to measure higher spatial frequencies by CCD array. In accordance with the theoretical estimation the modulation transfer function of the ideal CCD array is given by function:

,

where n - is spatial frequency of detected interference pattern and D - is linear size of CCD element.

To verify with theoretical result we have measured the MTF of our CCD array. For this purpose we have used our FS model with the He-Ne laser as light source. The CCD response was measured under different tilt angles between interferometer mirrors. Under such conditions CCD array detects sinusoidal interference pattern of spatial frequency n , which is a function of mirrors tilt angle. From FFT computations we can easily obtain the value of spatial frequency and ratio of it amplitude to the amplitude of zero frequency.

Normalized obtained MTF of CCD array is shown at Fig.3. Modulus of MTF was calculated by

where A_max , A_min - maximum and minimum values of measured signal in interferograms of frequency n .

The experimental curve lies somewhat lower than the sinc function, which is predicted by the standard theory. On our mind, this difference may be connected with the sensitivity pixel nonuniformity and charge transfer inefficiency in CCD that leads to the equivalent enlargement of detector element dimension.¹ For example, triangle response function of the element can be described by sinc² function.

The similar results were obtained with CCD TV camera. We have used SONY PIH-750 camera with CCD image sensor ICX045 containing 500X582 active pixels, framegrabber and PC. In Fig.4 we show experimental data and FFT computation results for two light sources - Hg-arc (one line - isolated by interference filter) and tungsten lamp. The interferograms were obtained by averaging of two lines in standard TV frame.

Fig.4 (a) Digitized intensity data of central raster in the interferograms; (b) power spectrum.

Osipov S.I., Lapchuk V. P. Laboratory model of static Fourier spectrometer for investigation of atmospheric emissions.  Proceeding SPIE, vol. 3237, p.158-161.

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