We use aberration theory to derive a generalized pupil function of the Golay3
imaging system when astigmatisms exist in its submirrors. Theoretical analysis
and numerical simulation using ZEMAX show that the point spread function (PSF)
and the modulation transfer function (MTF) of the Golay3 sparse aperture system
have a periodic change when there are piston errors. When the peak–valley value
of the wavefront ()
due to the tilt error increases from zero to ,
the PSF and the MTF change significantly, and the change direction is determined
by the location of the submirror with the tilt error. When
becomes larger than , the PSF and the MTF
remain unvaried. We calculate the peaks of the
signal-to-noise ratio (PSNR)
resulting from the piston and tilt errors according to the Strehl ratio, and
show that the PSNR decreases when the errors increase.
© 2013 Optical Society of America
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