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.