Method for Calculating the Offner Compact-Size Spectrometer

Significant advances in development of the optical wavelength range require high-quality optical systems to create optoelectronic equipment on their basis characterized by high speed and information capacity. A method for calculating a compact-size Offner spectrometer was developed having the advantages of its compactness, maintaining high optical characteristics and having relatively low cost in comparison with the large-size equipment. The method is based on using the Rowland circles and the coma and astigmatism correction in the image plane. Analytical expressions were obtained making it possible to calculate design parameters of the spectrometer optical scheme. Two examples of calculating optical systems for visible and infrared ranges were considered. Calculated systems were simulated in the Zemax software program. To evaluate the synthesized optical models image quality, the confusion spot radius in the image plane was used. It is demonstrated that the confusion spot radius value does not exceed the value of the radiation receiver pixel size in the considered spectral ranges. Optimization was carried out for the IR spectrometer according to overall dimensions in order to improve the design manufacturability. It is shown that the principles laid down in the method development are effective, and the method itself could be used in design and development of new small-size hyperspectral optoelectronic equipment

References

[1] Arkhipov S.A., Zavarzin V.I., Senik B.N. Developing and fabricating optical systems for a prospective remote-earth-probe spacecraft. J. Opt. Technol., 2013, vol. 80, no. 1, pp. 25--27. DOI: https://doi.org/10.1364/JOT.80.000025

[2] Prieto-Blanco X., Montero-Orille C., Couce B., et al. Analytical design of an Offner imaging spectrometer. Opt. Express, 2006, vol. 14, pp. 9156--9168. DOI: https://doi.org/10.1364/OE.14.009156

[3] Golovin A.D., Demin A.V. Simulation model of a multichannel Offner hyperspectrometer. Komp’yuternaya optika [Computer Optics], 2015, vol. 39, no. 4, pp. 521--528 (in Russ.). DOI: https://doi.org/10.18287/0134-2452-2015-39-4-521-528

[4] Kazanskiy N.L., Kharitonov S.I., Doskolovich L.L., et al. Modeling the performance of a spaceborne hyperspectrometer based on the Offner scheme. Komp’yuternaya optika [Computer Optics], 2015, vol. 39, no. 1, pp. 70--76 (in Russ.). DOI: https://doi.org/10.18287/0134-2452-2015-39-1-70-76

[5] Gorbunov G.G., Demin A.V., Nikiforov V.O., et al. Hyperspectral apparatus for remote probing of the Earth. J. Opt. Technol., 2009, vol. 76, no. 10, pp. 651--656. DOI: https://doi.org/10.1364/JOT.76.000651

[6] Kim S.H., Kwo D., Lawrence G., et al. Design and construction of an Offner spectrometer based on geometrical analysis of ring fields. Rev. Sc. Instrum., 2014, vol. 85, no. 8, art. 083108. DOI: https://doi.org/10.1063/1.4892479

[7] Mouroulis P., Green R.O., Chrien T.G. Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information. Appl. Opt., 2000, vol. 39, no. 13, pp. 2210--2220. DOI: https://doi.org/10.1364/AO.39.002210

[8] Zavarzin V.I., Li A.V. Calculation of the centered reflecting objective with eccentrically located image field. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2016, no. 2 (107), pp. 103--116 (in Russ.). DOI: http://doi.org/10.18698/0236-3933-2016-2-103-116

[9] Zemax 13 --- PO dlya analiza i proektirovaniya opticheskikh system [Zemax 13 --- software for designing optical systems]. Available at: https://www.zemax.com (accessed: 16.08.2021).

[10] Arkhipov S.A., Zavarzin V.I., Malykhin V.A., et al. Alignment and calibration of long-focus three-mirror lens with eccentric position of image field. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2009, no. 4 (77), pp. 24--36 (in Russ.).

[11] Zavarzin V.I., Li A.V. Quality control of large-scale mirror objectives with eccentric image field. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2014, no. 6 (99), pp. 39--48 (in Russ.). DOI: http://doi.org/10.18698/0236-3933-2014-6-39-48

[12] PTC MathCAD Prime 7 --- matematicheskoe PO dlya inzhenernykh raschetov [PTC MathCAD Prime 7 --- math software for engineering computations] (in Russ.). Available at: https://www.mathcad.com/ru (accessed: 16.08.2021).

[13] Sellar R.G., Boreman G.D. Comparison of relative signal-to-noise ratios of different classes of imaging spectrometers. Appl. Opt., 2005, vol. 44, no. 9, pp. 1614--1624. DOI: https://doi.org/10.1364/AO.44.001614

[14] Offner A., Decker W.B. An f.1.0 Camera for astronomical spectroscopy. J. Opt. Soc. Am., 1951, vol. 41, no. 3, pp. 169--172. DOI: https://doi.org/10.1364/JOSA.41.000169

[15] Mouroulis P., Wilson D.W., Maker P.D., et al. Convex grating types for concentric imaging spectrometers. Appl. Opt., 1998, vol. 37, no. 31, pp. 7200--7208. DOI: https://doi.org/10.1364/ao.37.007200