ON-ORBIT MTF ESTIMATION METHODS FOR SATELLITE SENSORS
LI Xianbin, JIANG Xiaoguang, Tang Lingli
Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing, 100080, China
lixianbin@aoe.ac.cn, Tel: (86)-10-62641267, Fax: (86)-10-62643022
KEYWORDS: Modulation transfer function (MTF); Point source/array method; Pulse method; Knife-edge method; Bi-resolution
method
ABSTRACT:
Modulation transfer function (MTF) is a standard measurement of imaging systems’ geometric performance. Prior to flight, the MTF
of satellite sensors is strictly measured in laboratory through various targets. However, it is important to estimate the MTF of satellite
sensors during their life cycles to determine if any system degradations occur over time. Therefore, almost all satellite management
organizations put much emphasis on MTF estimation and analysis. However, remote sensing data quality analysis and control in
China is not emphasized until recent years. As part of Sky-To-Earth System of Systems, we systematically research MTF estimation
methods and development on-orbit payload MTF test module. This paper first reports 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, and their advantages and drawbacks. Then, we give an example of MTF
estimation result using knife-edge method and pulse method.
1 INTRODUCTION
The spatial resolution of satellite-borne sensors is usually
described by the Modulation Transfer Function (MTF), i.e. the
Fourier Transform (FT) of the impulse response (system’s
response to an ideal point source or Point Spread Function
(PSF)). Prior to flight, the MTF of satellite sensors is strictly
measured in laboratory through various targets. However, this
important parameter for image quality has to be checked
on-orbit to be sure that launch vibrations, space condition when
imaging, the performance variation of detectors and other
components have not spoiled the sharpness of the images.
Therefore, it is important to estimate the MTF of satellite
sensors during their life cycles to determine if any system
degradations occur over time.
Moreover, Remote sensing is complex information acquire
process, and each step will introduce some degradation to the
acquired image, including ground sampling, atmosphere scatter
and absorption, remote sensors’ effect (diffraction, aberrations,
focusing error, charge diffusion, platform motion, et al), image
transmission, ground image process, and so on. All these
degradations’ cumulative effect during image acquisition and
transmission is described by system overall Modulation
Transfer Function (MTF) which can be estimated from remote
sensing imagery. Therefore, MTF is useful to make a
deconvolution filter whose purpose is to enhance image
contrast by ground processing.
There have many on-orbit MTF estimation methods been
studied and implemented. Usually, we divide those methods
into point source/array method, knife-edge method; pulse
method according to their targets. Furthermore, 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
MTF. This is so-called bi-resolution method. Thus, this paper
introduces their target deployment/selection standards, data
processing steps, and their advantages and drawbacks. Then,
we give an example of MTF estimation result using knife-edge
method and pulse method.
2 POINT SOURCE/ARRAY METHOD
2.1 The principle of point source/array method
For line position (space) invariant system, the image produced
by image system g(^,^) can be represented by the convolution
of system response psF(x,y) ar| d input scene f(x,y) > given by:
g(x,y) = f(x,y) * PSF(x,y) + n(x,y)
Where n(x,y) is system introduced noise. According to
Convolution Theorem, the equation can be expressed in
frequency domain as:
G(w.v) = F{u, v) • OTF (u, v) + N(u, v)
Where g(w.v) , F(«,v) » OTF{u,v) , N(u,v) are the Fourier
transform of g ( x ,y) , f(x,y) > PSF(x,y) , n(x,y) respectively.
According to optical theory, MTF is the modulus of OTF
(called Optical Transfer Function).
Therefore, if we deploy a spotlight or convex properly, the
system’s response to the point source can be treated as Point
Spread Function (PSF). However, limited by system’s spacing
interval, the imaging system’s response to point source is
undersampled, which leads to aliasing effects on the MTF
when it is computed directly using Discrete Fourier Transform.
The cheapest way to overcome aliasing problem is to use a
model. Another widely-used way is to properly deploy an array
of point source with different sample phase, and align these
system’s responses to a common reference according to the
sample phase to get oversampled PSF.
Figure 1 illustrates that system’s response to point source with
different phase get quite different response (see a-d), aligning
those responses according to peak locations gets oversampled
1-D system’s response (see e).
