Abstract. This paper
describes an algorithm of searching the aberration coefficients from defocused
image of a point source. In proposed approach, the wave front aberrations which
are caused by optics misalignment are represented by Zernike polynomials.
Zernike polynomials coefficients which indicate lens alignment can act as
criteria of an optical systems quality. Implementation of the algorithm
requires the ‘direct task’ solution in order to get the aberrated image using the values of the Zernike coefficients.
In the article several possible approaches to obtain
the image of a point spread function which is calculated from the values of the Zernike’s coefficients are
presented: geometric, diffraction by the Kirchhoff integral, diffraction by
Nijboer-Zernike approach. Comparison of the methods mentioned above was made at
the base of the algorithm’s time response
and the resulting image accuracy. Algorithm
proposed for finding aberrational Zernike
coefficients is based on the ‘direct task’ solution and comparison based on the discrepancy criterion
between obtained image and the actual image of the real lens step-by-step. The
geometrical approach was used for the ‘direct task’ solution as the fastest and
ideologically simplest algorithm. The approach was tested on the axial
catadioptric Ritchey–Chrétien lens. Estimation of the Zernike
coefficients gives an ability to define current relative positions of the lens
optical components. This allows the system’s alignment to be done.
Key words: aberration, Zernike
polynomials,
lens adjustment, Earth remote sensing.
References
1. Liu H., Li
G. OFDM-Based Broadband Wireless Networks. Hoboken: John Wiley & Sons.
2005. 251 p.
2. Bakulin
M.G., Kreindelin V.B., Shloma A.M., Shumov A.P. Technologia OFDM. [OFDM
Technology]. Moscow, Telecom Publ., 2016. 352 p. (In Russian)
3. Akhmed N., Rao K.R. Ortogonalnye
preobrazovaniya pri tsifrovoy obrabotke signalov. [Orthogonal
transformations in digital signal processing]. Moscow, Svyaz Publ. 1980. 248 p.
(In Russian).
4. Shinakov
Y.S. Power spectral density of interference caused by
nonlinear distortions in devices with amplitude-phase conversion. Journal
of Communications Technology and Electronics, 2013, Vol. 58, No.10, pp.
1024-1034. DOI:
10.1134/S106422691310001X
5. Shinakov Y.S. Two methods of
output signal power calculation for devices with amplitude-phase conversion.
Radiotechnika - Radioengineering, 2016, No. 2, pp. 66-71. (In
Russian)
6. Nazarov
L.E., Zudilin A.S. Estimating the power and efficiency of
intermodulation interferences under the OFDM-signal-envelope limitation.
Journal of Communications Technology and Electronics, 2015, Vol. 60,
No.5, pp. 489-495. DOI:
10.1134/S1064226915050071
7.
Nazarov L.E., Zudilin A.S. Techniques for estimating the
power of the intermodulation interferences of orthogonal frequency-division
multiplexing signals. Journal of Communications Technology and
Electronics, 2014, Vol. 59, No.2, pp. 158-163. DOI:
10.1134/S1064226914020041
8. Nazarov
L.E., Zudilin A.S. Techniques for narrow band noise reduction for OFDM signals. Izvestija
vysshih uchebnyh zavedenij.Elektronika - Russian microelectronics, 2013, No. 6
(104), p. 45-51. (In Russian)
9.
Kalinin V.I., Radchenko D.E., Cherepenin V.A. The error-performances of digital
channels based on continue noise signals under spectral modulation. Radiotechnika-Radioengineering,
2015, No. 8, pp. 84-94. (In Russian)
10. Fink L.M. Teoriya peredachi discretnykh soobschenii. [The
theory of discrete message transmission]. Moscow, Sov. Radio Publ. 1970. (In
Russian).
11. Widrow B., Stearns S.D. Adaptive signal processing. Prentice-Hall,
Inc. Englewood Cliffs, N.J. 07632. 1985.
12. Zudilin
A.S., Nazarov L.E. Analysis of noise immunity for signal constructions based on
ofdm and error-correcting codes robusted for signal influence concentrated on a
range. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2017. No.11.
http://jre.cplire.ru/jre/nov17/4/text.pdf
(In Russian)
13. Nazarov
L.E., Sheglov M.A. The Characteristics of Full and Shortened Immune-Noise LDPC
Codes Based on Finite-Geometry. Uspekhi sovremennoy radioelektroniki - Achievements of Modern Radio Electronics.
2017. No. 6. pp.23-30. (In Russian)
14. TM synchronization and
channel coding - summary of concept and rationale. Information report CCSDS
130.1-G-1. Green Book. 2006.