5 BI-RESOLUTION METHOD 
5.1 The principle of bi-resolution method 
If we can acquire image couples of the same landscape in the 
same or similar spectral band with two different spatial 
resolutions, the higher resolution image can stands for the 
landscape so that the ratio of the image spectra gives the lower 
resolution sensor’s MTF. Its theory basis is that the MTF of 
reference image is nearly 1 at the frequency of interest in low 
spatial resolution image and therefore is negligible. 
\ im ageL„„(u,vi 
estMTF Low (u,v) = 
image Kcf {u,v)\ 
_ |scenetu^MTF^u^) 
(a) 
| scene(u, v)| MTF Ref (u, v) 
MTFlo W {u,v) 
(b) 
Ml'F Rtf (u,v) 
= MTFuwiU’V) 
Where v ) are spatial frequency coordinates in units of cycles 
per pixel, MTF Low (u,v) - MTF Rc/ (u,v) are MTF of low spatial 
resolution image and reference image respectively. 
image lur (u,v) * s the spectra image of low spatial resolution 
image, which is the multiplication of the observed scene 
spectrum and MTF, image R (u, v) * s the spectra image of 
reference image. Cancellation of term | iC g„ e ( U)V )| in equation 
(a) leads to equation (b). Because MTFr ( wv )is nearly 1, the 
ratio of the image spectra gives the lower resolution sensor 
MTF. 
5.2 Target deployment/selection standards for bi-resolution 
method 
There is no special requirement for bi-resolution MTF 
estimation method targets. However, to get ideal result, it’s 
better to choose an image contain a variety of features, such as 
roads, shorelines, buildings, etc. that exhibit high spatial 
frequency content. 
Another requirement is that the spatial resolution difference 
should be as much as possible to insure that the higher 
resolution image can stands for the true landscape. 
5.3 Data processing steps for bi-resolution method 
This method starts with the image simulation with an initial 
PSF, This PSF is to be sampled as the high resolution image. 
Convolving the high resolution image with this PSF and 
undersampling at the low resolution sampling rate yields an 
image which is compared to the low resolution image through a 
least square residual computation. The initial parameter value is 
then modified in order to minimize this least square residual, 
according to a classical least square minimization algorithm. 
The iterative process will end when the relative residual change 
between two iterations goes below a threshold level to be fixed 
by the user. Then, the PSF can be treated as the PSF of low 
resolution sensor. A Fourier Transform is applied to the PSF 
and normalized to obtain corresponding MTF. 
6 ANALYSIS AND COMPARISON 
We have introduced the principle of several widely-used 
on-orbit MTF estimation methods (including point source/array 
method, knife-edge method; pulse method, and bi-resolution 
method), their target deployment/selection standards, data 
processing steps. Each method has its applicability and 
limitations. We should choose the optimal method according 
the spatial resolution of sensor and target condition. 
1) For point source/array method, it is suitable for 
high/moderate resolution sensor MTF estimation. We can 
directly obtain 2-D PSF and MTF, but this method requires 
deploying special targets and the cost is relatively high. This 
method has been successfully applied to MTF estimation of 
Landsat/TMN SPOT^ Quickbird. 
2) The target for knife-edge method is relatively easy to 
deploy or select. Very high SNR can be obtained leading to 
accurate MTF estimation. But for low resolution sensors, it is 
difficult to find a large enough target. 
3) For low resolution sensors, pulse method is a good choice. 
While good results can be obtained, limiting factors including 
controlling background regions on either side of the pulse, 
avoiding zero-crossing when designing the target, and directly 
deriving the PSF. 
4) Bi-resolution method requires acquiring image couples of 
the same landscape in the same or similar spectral band with 
two different spatial resolutions simultaneously. The data 
processing of this method is relatively complex, and it is 
sensitive to noise and aliasing. 
7 EXAMPLE 
In on-orbit MTF estimation module, knife-edge method and 
pulse method is the .primary MTF estimation methods. There 
we give an example of MTF estimation result of SPOT/Pan 
image using knife-edge method and pulse method. 
7.1 Knife-edge method target and result 
The targets used for knife-edge method is runway in Dalian 
airport. Three different targets are given in figure 4 and the 
MTF estimation results are shown in figure5.