# Full text: Mapping without the sun

```Fig 3 The relationship between the location of Nyquist frequency and pulse width
3.3 Data processing steps for pulse method
The data processing for pulse method includes following steps:
1) Image preprocessing: according to the characteristic of
pulse image, remove the noise existing in pulse image using
threshold method and median filter.
2) Edge detection: numerically differentiate each image
profile to detect the location of maximum slope.
3) Least-square error fitting line for subpixel edge locations:
It has been assumed that the subpixel edge locations should lie
along a straight line. Therefore, all edge cross sections were
forced to a straight line by perform a least squares fit.
4) Edge alignment: first interpolates the edge profiles to a
subpixel interval, and then averages these image profiles after
alignment according to edge location to obtain LSF.
5) Fourier Transform: calculates the Fourier Transform of
trimmed LSF and generated ideal square pulse function.
6) MTF estimation: divide the Fourier Transform spectra of
LSF by the Fourier Transform spectra of ideal square pulse
function and normalized to obtain the corresponding MTF.
4 KNIFE-EDGE METHOD
4.1 The principle of knife-edge method
The response of system to ideal knife-edge is called Edge
Response Function (ERF), which is the signal spreading along
the direction perpendicular to the edge. The theory basis of
knife-edge method is that the differentiation of ERF is LSF.
Suppose knife-edge can be express as:
Then, the output of system is:
g(x) = /(x) * LSF(x) = £/(r) ■ LSF(x - x)dr
Thus: g ( x ) = ^LSF(x-r)dT
Assuming t = x — t, then r — x — t .Therefore:
g(x)= JT LSF(t)d(x -t)= [^LSF{t)dt
Where g(x:) is so-called ERF(x) ■ Thus:
ERF(x) = ^LSF(t)dt
Equivalently:
<wm
dx
In conclusion, the differentiation of ERF is LSF.
4.2 Target deployment/selection standards for knife-edge
method
The target for knife-edge method should have the following
characteristics:
1) A good edge target consists of a ‘dark’ or low-reflectance
side, and a ‘bright’ or high-reflectance side. The
high-reflectance side ideally has a reflectance level that
provides a sensor response near the high end of its dynamic
range; a rule of thumb is >75% of the dynamic range of the
sensor. The dark side of the edge should be a reflectance level
as low as possible, say less than 5%.
2) Because most high quality will not have a PSF that
extends beyond a distance of a few GSI, a reasonable rule of
thumb is that the target should extend 7-10GSI beyond the
edge.
3) Edge target need to be well controlled in terms of
homogeneity and contrast. The homogeneous regions should be
uniform and isotropic, and the contrast across the edge must as
large as possible. Simulations have shown that an SNR>50 is a
reasonable lower threshold.
4) Often orientation becomes critical due to the imaging
system being discrete. If the edge is parallel with the sample
grid, no matter how long the edge is, only on a regular grid of
locations have samples of the system response. If the target has
a slight angle with the sample grid, we can get subsample
reconstruction of the system response, and then the ERF can be
reconstructed at a much finer resolution than the sample
distance
4.3 Data processing steps for knife-edge method
The data processing for knife-edge method includes following
steps:
1) Image preprocessing: according to the characteristic of
knife-edge image, remove the noise existing in knife-edge
image using threshold method and median filter.
2) Edge detection: numerically differentiate each image
profile to detect the location of maximum slope.
3) Least-square error fitting line for subpixel edge locations:
It has been assumed that the subpixel edge locations lie along a
straight line. Therefore, all edge cross sections were forced to a
straight line by perform a least squares fit.
4) Edge alignment: first interpolates the edge profiles to a
subpixel interval, and then averages these image profiles after
alignment according to edge location to obtain ERF.
5) LSF derivation: numerically differentiate ERF to obtain
system’s LSF.
6) MTF estimation: calculates the Fourier Transform of
trimmed LSF and normalized to obtain the corresponding MTF.
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