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Mapping without the sun
Zhang, Jixian

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Fig 1 The reconstruction
2.2 Target deployment/selection standards for point
source/array method
For point source method, the primary consideration is the
at-sensor irradiance intensity. The following standards should
be obeyed when deploy point source target:
1) Properly design the irradiance intensity to avoid the
saturation of image system. Furthermore, to get enough
contrast and SNR, the point source should be designed so that
the peak sensor response is on the order of 75% of its dynamic
2) A complicating factor for point source method is that
many high spatial resolution sensors are pointable. Therefore,
it’s better to use diffusion bodies or convexes as point sources.
For point array methods, besides the intensity of point
sources, there are two major considerations need to be
1) The number of point sources should be as much as
possible, which is restricted by the size of target, cost, etc.
Experience indicates that 15-20 point sources can obtain
reasonable result.
2) There must be enough distance between different point
sources so that system’s response to different point sources
can’t overlap. For many systems, the PSF does not extend over
3-GSI, thus, a minimum mirror separation of 5-GSI should be
Figure 2 gives an example of point array target. The point
sources are diffusion bodies. There are total 16 point sources in
a 4X4 arrange style. The distance between two nearest point
sources is 5.25 pixels, and there are 0.25 pixels sample phase
differences between two nearest point sources.
Fig 2 Point array target deploy example
2.3 Data processing steps for point array method
Usually, the data processing for point array method uses
parametric approaches. The basic steps include:
1) Determines peak location of each point source data set to
subpixel accuracy using a parametric two-dimensional model
(Gaussian model).
2) The individual point source data sets are aligned along
of oversampled PSF
their model-estimated center positions to a common reference.
3) The 2-D model is applied again to estimate system’s
oversampled PSF.
4) A Fourier Transform is applied to the PSF and normalized
to obtain the corresponding MTF.
3.1 The principle of pulse method
Image system’s response to ideal line is Line Spread Function
(LSF), which is the integration of PSF in the direction
perpendicular to the line. According to optical theory, the
modulus of the Fourier Transform of LSF is corresponding 1-D
MTF. However, it is impossible to get infinitely narrow line
source. Thus, the Fourier Transform of LSF obtained from
image should be corrected according to the width of input pulse.
The approach divide the spectra of LSF obtained from image
by the spectral of ideal square pulse with the same width to
obtain corresponding MTF.
3.2 Target deployment/selection standards for pulse method
The target for pulse method should have the following
1) Pulse target should consist of a uniformly bright region
with two homogeneous dark regions. The boundaries between
the bright and dark regions are straight edges.
2) The orientation of the pulse target must be maintained so
that the oversampled pulse response can be obtained from
imagery (about its principle see section 4.2).
3) The length of pulse target should be as long as possible, at
least obtain several ‘slices’ of the PSF in the orthogonal
4) The pulse target width must be designed carefully to place
the zero-crossings at locations where the value of the MTF is
not critical to evaluating system performance (especially not at
Nyquist frequency).
When calculating system MTF, a Fourier Transform of the
pulse response and ideal squre pulse function is required. Since
the well-known Fourier Transform of a square pulse function is
a sine function, it is necessary to deal with zero-crossings. It is
apparent that the width of pulse target should be as narrow as
possible to avoid zero-crossings, say one GSI or less. However,
the difficulty is that the strength of the signal received by the
sensor from the narrow pulse width decreases linearly as the
width of the pulse. As a result, the SNR is compromised and a
good estimate can not be obtained. Practice has shown that a
pulse width of 3-GSI is optimal for this type of target. With this
width, a good tradeoff is reached between obtaining a strong
signal and maintaining ample distance from placing a
zero-crossing at the Nyquist frequency (see figure 3).