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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 4 — Feb. 15, 2010
  • pp: 3531–3545
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Improvement of the edge method for on-orbit MTF measurement

Françoise Viallefont-Robinet and Dominique Léger  »View Author Affiliations


Optics Express, Vol. 18, Issue 4, pp. 3531-3545 (2010)
http://dx.doi.org/10.1364/OE.18.003531


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Abstract

The edge method is a widely used way to assess the on-orbit Modulation Transfer Function (MTF). Since good quality is required for the edge, the higher the spatial resolution, the better the results are. In this case, an artificial target can be built and used to ensure a good edge quality. For moderate spatial resolutions, only natural targets are available. Hence the edge quality is unknown and generally rather poor. Improvements of the method have been researched in order to compensate for the poor quality of natural edges. This has been done through the use of symmetry and/or a transfer function model, which enables the elimination of noise. This has also been used for artificial target. In this case, the use of the model overcomes the incomplete sampling when the target is too small or gives the opportunity to assess the defocus of the sensor. This paper begins with a recall of the method followed by a presentation of the changes relying on transfer function parametric model. The transfer function model and the process corresponding to the changes are described. Applications of these changes for several satellites of the French spatial agency are presented: for SPOT 1, it enables to assess XS MTF with natural edges, for SPOT 5, it enables to use the Salon-de-Provence artificial target for MTF assessment in the HM mode, and for the foreseen Pleiades, it enables to estimate the defocus.

© 2010 OSA

1. Introduction

The spatial resolution of satellite-borne cameras is usually described by the Modulation Transfer Function (MTF) [1

1. M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983). [CrossRef]

]. This important parameter for image quality has to be checked in orbit in order to be sure that launch vibrations, transition from air to vacuum, or thermal state have not spoiled the sharpness of the images. In some cases, it can lead to refocusing decision.

This paper deals with one of the methods used for on-orbit MTF assessment, called the edge method, the knife-edge method, or the slanted-edge method. This method is widely used for laboratory measurements and may be implemented in various manners. For on-orbit MTF assessment, it requires a slanted edge as explained in section 2. It has been used for numerous space sensors such as Landsat TM [2

2. W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

], MOS-1 MESSR [3

3. K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987). [CrossRef]

], or more recently IKONOS [4

4. T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).

].

This paper presents improvements of the edge method for measuring the on-orbit MTF. It concerns the spectral approach [5

5. H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

], which is less known than the derivative one [3

3. K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987). [CrossRef]

], [4

4. T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).

], [6

6. H. Hwang, Y.-W. Choi, S. Kwak, M. Kim, and W. Park, “MTF assessment of high resolution satellite images using ISO 12233 slanted-edge method”, Proc. SPIE 7109, 710905–1-710905–9 (2008).

]. After the recall of the method, modifications are presented relying on symmetry assumptions and Point Spread Function (PSF) [1

1. M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983). [CrossRef]

] model. The parametric model used is then described. At this stage, the process to derive the PSF model from the transfer function parametric model and to apply it is explained. Various results, concerning satellites of the French Space Agency, are presented to illustrate the improvement of the method: SPOT 1 XS MTF assessment, SPOT 5 HM mode MTF assessment, and Pleiades defocus assessment.

2. The edge method

Considering the sensor as a linear system versus radiance, the relation between the landscape and the image is simply:
i(x,y)=l(x,y)h(x,y)
(1)
where i(x,y) stands for the image,

l(x,y) stands for the landscape,

h(x,y) is the Point Spread Function of the sensor,

⊗ is the convolution product.

A classical way to deal with a convolution product is to apply a Fourier Transform, which leads to:
I(fx,fy)=L(fx,fy).H(fx,fy)
(2)
where I(fx,fy) stands for the Fourier Transform of the image,

L(fx,fy) stands for the Fourier Transform of the landscape,

H(fx,fy) is the Transfer Function of the sensor.

The sensor behavior is known to be similar to a low-pass filter without phase shift [7

7. C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

]. This is why the Transfer Function is usually reduced to the Modulation Transfer Function defined as the modulus of the Transfer Function.

I(fx,fy)/L(fx,fy)=H(fx,fy)
(3)

In the case of the edge method [5

5. H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

], the term l(x,y) is close to the Heaviside function, hea(x) or hea(y):

l(x,y)=a .hea(x)+b
(4)

In the Fourier domain, it comes:

L(fx,fy)=a.Hea(fx)+b .δ(fx)
(5)

Considering the noise, Eq. (1) becomes:

i(x,y)=l(x,y)h(x,y)+n(x,y)
(6)

In the Fourier domain, it leads to:

I(fx,fy)=L(fx,fy).H(fx,fy)+N(fx,fy)
(7)

So, Eq. (3) becomes:

I(fx,fy)/L(fx,fy)=H(fx,fy)+N(fx,fy)/L(fx,fy)
(8)

In most cases, including the edge case, L(fx,fy) is a decreasing function of the frequency and thus the noise term increases along with the frequency, spoiling the transfer function assessment for high frequencies.

In the Fourier domain, the relation becomes:

I(fx,fy)=[L(fx,fy).H(fx,fy)]W(fx,fy)comb(fx,fy)
(10)

The convolution by the comb produces aliasing. One way to overcome this problem is to use an edge with a slight inclination relative to the row or column direction [5

5. H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

]. This is used to build an oversampled 1-D edge image as explained in Fig. 1
Fig. 1 Principle of 1-D oversampled edge response
.

The windows have to be chosen so that:L(fx,fy)⊗W (fx,fy) ≠ 0 for all frequencies and not far from L(fx,fy).

All this leads to:

I(fx)/[a.Hea(fx)+b .δ(fx)]W(fx)H(fx)
(11)

The same relation can be written for fy. Such software has been developed by Onera using Matlab under CNES studies. It has been applied with natural edges for SPOT 4 without success [8

8. P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998). [CrossRef]

] and with the Salon-de-Provence artificial target for SPOT 5 THR MTF assessment [9

9. D. Léger, F. Viallefont, P. Déliot, and C. Valorge, “On-orbit MTF assessment of satellite cameras”, in Post-launch calibration of satellite sensors, Morain and Budge, ed. (Taylor and Francis group, London, 2004).

]. A new version, with an improved user interface named MEFISTO, has been developed by THALES-IS for CNES.

3. Changes of the method

The analyze of the SPOT 4 MTF measurement failure with natural edges shows that such edges are not uniform enough and often, their inclination doesn’t correspond to regular sampling. The uniformity is often better for the dark side of the edge than for the light side. Assuming that the PSF is symmetrical, it is possible to find the symmetry point of the oversampled and noisy edge and then to replace the less uniform side by the radiometric level obtained by symmetry with the more uniform side.

For the inclination, in the ideal case of Fig. 1, the sequence is composed with a whole number (4 in this case) of rows. However, it may be impossible to find a whole number of rows corresponding to the sequence for natural edges. Up to now, the process consisted in combining the Ns rows of the sequence, Ns being the whole number the closest to the actual number of rows of the sequence. This made the number of rows Ns equal to the oversampling rate Nr. Now, the user chooses the oversampling rate Nr, not too far from Ns and then each phase of the row of the sequence is placed in the Nr grid. Some cases of Nr ≠ Ns, may lead to incomplete sampling. As FFT requires regular sampling, the user has to choose between spline interpolation and model fitting. The spline interpolation affects the MTF assessment all the more so the noise is high and the oversampling rate is small. In the model fitting case, all the edge samples are replaced by the samples deduced from a parametric transfer function model as explained in section 5. Even though the number of rows of the sequence is very close to an integer, which would lead to Nr = Ns, the model fitting enables to eliminate the noise due to the non-uniformity of the dark or light areas.

4. Transfer function parametric model

Some changes of the method rely on a parametric transfer function model. Our model, valid for a circular pupil, is built by multiplication of the following elementary transfer functions:

Hdiffraction=2π[arccos((fx2+fy2)1/2DλF)(fx2+fy2)1/2DλF(1((fx2+fy2)(DλF)2))1/2]
(12)
Hoptics=exp(αx2fx2+αy2fy2)
(13)
Hdefocus=2J1(πΔN(fx2+fy2)1/2[1λN(fx2+fy2)1/2])πΔN(fx2+fy2)1/2[1λN(fx2+fy2)1/2]
(14)
Hdetector=sinc(πfxfsx)×sinc(πfyfsy)
(15)
Hmoving=sinc(πfyfsy)
(16)

So,

Hmodel=Hdiffraction.Hoptics.Hdefocus.Hdetector.Hmoving
(17)

The expression for Hdefocus [Eq. (14)] is taken from [10

10. W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).

]. Classically, N is the aperture number and λ the central wavelength. αx or αy (depending on the direction of the perpendicular to the edge) and the defocus Δ are the parameters to find. fx and fy are the spatial frequencies corresponding to the rows and to the columns. fsx and fsy are the sampling frequencies along the directions corresponding respectively to x and y.

5. Description of the process

The kernel of the process consists in fitting an edge computed thanks to the transfer function parametric model with the actual 1-D edge. First, an ideal edge is computed corresponding to Eq. (4). Then, the 1-D transfer function Hmodel is computed, according to Eq. (17) in the direction perpendicular to the edge with initial parameter values, αx or αy, and Δ, chosen by the user. A Line Spread Function (LSF) [1

1. M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983). [CrossRef]

] is computed by inverse Fast Fourier Transform of the transfer function. It is then convolved to the ideal edge as in Eq. (1). This produces the model edge response. Then the quadratic distance between the actual edge and the model edge is computed and minimized via the IDL POWELL procedure. The minimization provides adequate values for the parameters αx or αy, and Δ.

6. First application: SPOT 1 XS1 and XS2 on-orbit MTF assessment

Before describing the application of the method to SPOT 1, let us recall relevant features of SPOT 1. SPOT 1 has two identical cameras on board named HRV1 and HRV2. The Ground Sampling Distance (GSD) of the cameras is 20 m for the multispectral mode (XS) and 10 m for the panchromatic mode (Pa). The multispectral mode enables to take three images in the spectral bands named XS1, XS2, and XS3 corresponding respectively to the green, the red, and the very near infrared.

For MTF assessment, a SPOT 1 HRV1 image over La Crau (4.87° E, 43.57° N), taken on 07 February 1998, has been selected. Three horizontal edges and three vertical edges have been extracted from the XS2 image using ENVI software. This has lead to six files named s1h1x2yy.oct where:s1 stands for SPOT 1,

h1 stands for HRV1,

x2 stands for XS2, and

yy = h1 for the horizontal edge number 1

h2 for the horizontal edge number 2

h3 for the horizontal edge number 3

v1 for the vertical edge number 1

v2 for the vertical edge number 2

v3 for the vertical edge number 3.

Figures 2
Fig. 2 Image around h1
5
Fig. 5 Image around v3
show areas around the extracted edges:

Fig. 3 Image around h2 and h3
Fig. 4 Image around v1 and v2

The features of the six edges are presented in the following Table 1

Table 1. Features of the edges

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:

The oversampled h1 edge is clearly unsymmetrical. It shows the strange (but known) behavior of the array number 1 of the instrument (Fig. 6
Fig. 6 1-D h1 edge
). This leads to a particularly low MTF (Fig. 8
Fig. 8 Results for horizontal edges
).

The h2 edge quality is good, but the inclination of the edge is rather strong. It should lead to an oversampling rate Nr equal to Ns that is to say 2, which is a little bit too small to avoid aliasing. As the edge is large enough, our IDL tool enables to achieve an oversampling rate Nr = 10 and thus to avoid aliasing. The fit of the model (Fig. 7
Fig. 7 Fit of SPOT model for 1-D h2 edge in XS2
with actual edge in solid line and model in dashed line) enables to eliminate the noise.

The h3 edge inclination is also rather strong and the edge has small sizes. The reachable oversampling rate is limited to Nr = Ns = 2, which is not enough. Finally, this edge will not be taken into account.

The result considered as HRV1 XS2 on-orbit performance is the MTF curve obtained with the h2 edge. The drop of MTF between array 1 and array 4 given by the on-orbit survey of the relative MTF is applied to the h2 result at 0.3fs, 0.5 fs being the Nyquist frequency. Figure 8 shows that the resulting point is in full agreement with the measurement corresponding to the h1 edge on the array 1.

The v1 and v2 edges exhibit areas with poor uniformity. An attempt has been made to use the symmetry (Fig. 9
Fig. 9 1-D v2 edge to be modified according to symmetry assumption and model assuming symmetry
), but the belonging of v1 and v2 to the array 1 makes the corresponding results suspicious. The v3 edge is located on the array number 4. Its quality is good. Its size and its inclination enable a good oversampling rate. The results given by this edge are considered as the on-orbit across-track performance.

Thanks to the model, on-orbit SPOT1 MTF has been assessed for the along-track direction. Beyond the SPOT results, this work probes the efficiency of the edge method change.

7. Second application: SPOT 5 HM MTF assessment

A brief presentation of SPOT 5 can be found in [11

11. A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003). [CrossRef]

]. Here, we recall only the GSD of SPOT 5 HRG cameras. The linear array push-broom system provides a 5 m-sampled image in a panchromatic band called HM. In fact, each HRG instrument can acquire two images with this GSD (HMA and HMB). The system provides also a 2.5 m-sampled image using the following process: The two 5 m images are interlaced, then interpolated on a 2.5 m x 2.5 m grid, and finally restored by a deconvolution filter to sharpen the final product. The 2.5 m band is called THR.

The 2.5 m GSD is small enough to use an artificial edge target that has been laid out by Onera and CNES at Salon-de-Provence in the south of France. The target looks like a checkerboard. This shape allows performing across-track and along-track measurements and distinguishing between upward and downward steps. The overall size of the target is 60 m × 60 m. The target is a tar pad painted with road paints. The white diffuse reflectance is about 0.50 and the dark one is 0.05.

During the commissioning phase of the satellite, in 2002, the camera MTF was assessed with a 2.5 m image of the edge target (Fig. 11
Fig. 11 SPOT 5 THR image of Salon-de-Provence target
).

The THR image used in MTF assessment was not the standard THR product because the deconvolution process modifies the MTF while the assessment goal was to check the instrument MTF. Therefore, a special treatment with only interlacing and interpolation was used to obtain the 2.5 m image. The need for a special treatment is clumsy for MTF routine assessment, which is conducted each year. It is easier to use the 5 m image in the standard HM band. Badly, the target is a bit tight to obtain the number of lines needed in the oversampling process (Fig. 1). Given the angle between the orbit track of the satellite and the edge inclination, the oversampling rate is three. Therefore, the minimum number of useful image lines is three. A useful line is a line across the target far enough from sides in order to avoid a mixing effect between target and background. Generally, there are only two useful lines. These two lines allow filling two points out of three in a regular grid with an oversampling rate Nr = 3. The missing points must be interpolated. Two methods are possible as explained in § 3: spline interpolation or model fitting. These two methods have been applied to HM images for the same date as THR image. We compare the three obtained curves: THR, HM with spline interpolation, and HM with model fitting, in Fig. 12
Fig. 12 Comparison of along-track results
and Fig. 13
Fig. 13 Comparison of across-track results
, for along-track and across-track respectively. The three results are very similar, peculiarly around Nyquist frequency. The THR curve and spline interpolated HM curves are very close. These curves show a difference with model HM curve in low frequencies. This is due to a calculation artifact. Indeed, the limited length of lines brings about a truncation effect, which brings about the rounded shape of the curves. The truncation effect can be written as the product of the LSF by a rectangular window. In the frequency domain, there is a convolution between the MTF and the Fourier transform of the rectangular window, i.e. a sine cardinal function. The rounded shape at low frequency is due to this sine cardinal function. There is not such a truncation in the model method. Moreover, the no-model curves stray from the model curve in high frequencies because of noise in the 1-D edge image. Using a model is a way to eliminate the noise.

The SPOT 5 results extend the SPOT 1 ones and demonstrate the interest of the change of the edge method: extension to edge inclination or size leading to incomplete sampling and noise decrease.

8. Third application: Pleiades defocus assessment

A description of Pleiades features can be found in [12

12. A. Rosak, C. Latry, V. Pascal, and D. Laubier, “From SPOT5 to Pleiades-HR: evolutions of the instrumental specifications”, in Proceedings of the 5th international conference on Space Optics, B. Warmbein, ed. (ESA SP-554, Noordwijk, Netherlands, 2004), 141–148.

]. Simulations have been made by P. Kubik in CNES in order to provide images representative of an ideal checkerboard target viewed by a camera having radiometric performances close to Pleiades ones. The inclination of the edges leads to an oversampling rate Nr = Ns = 10. More precisely, the simulated images correspond to the MTF given by:

  • Aperture number N = 19,
  • Ratio of diameter of the occultation to the pupil diameter = 0.3,
  • Perfect square detectors 13 x 13 µm2 wide,
  • No moving effect (Hmoving = 1),
  • Defocus = 0 or 400 µm.

The kernels corresponding respectively to images without and with defocus (rep_pa and rep_pa_defoc) have been provided. Fitting the MTF model with the FFT of these kernels enables to estimate the applied coefficient α = αx = αy = 1.583. For each image, two vertical edges have been extracted, a « large » one with 82 columns and 70 rows, and a « small » one with 42 columns and 11 rows.

The nomenclature of the extracted edges is given in the following Table 2

Table 2. Nomenclature of the edges

table-icon
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:

All extracted images have been processed:

  • First directly, that is to say without the use of a model,
  • Then using the transfer function parametric model (an “m” is added at the end of the name).

The obtained MTF curves have been compared. These curves are representatives of the MTF in the direction of the perpendicular to the edge and they are affected by the windowing effect, as edges are not infinite. Hence, the row or column MTF must be computed using the parameters values found.

An example of obtained MTF curves is presented in Fig. 14
Fig. 14 MTF curves for small edge image
. It is easy to see that curves with or without model are well superimposed. It is also easy to see that the noise disturbs the measurements from 0.35fs for the small edge. In this case, the model is then useful to eliminate the sensor noise. For the large edge, the averaging of the rows having the same phase enables to reduce the noise (Fig. 15
Fig. 15 MTF curves for large edge image
). The obtained parameters and corresponding row MTF for Nyquist frequency are presented in Table 3

Table 3. Obtained model parameters and MTFx

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.

This table shows that minimization doesn’t allow to distinguish between parameter α and defocus Δ. Moreover, right defocus and α values are not obtained even though they are taken for input of the minimization.

A possible explanation is that the behavior of the defocus term Hdefocus and of Hoptics are different enough only for high frequencies (typically above Nyquist) or for large defocus. As the noise disturb the MTF curve before Nyquist frequency, it becomes difficult, in this case of fairly small defocus, to make the right distinction between α and the defocus Δ.

Complementary simulated images, corresponding to a large defocus (1200 µm), have been provided by CNES. The obtained MTF curves have been superimposed and the dimensioning case (for a small edge) is presented in Fig. 16
Fig. 16 Results with and without model for a small edge and a 1200 µm defocus
. Curves with and without model are well superimposed up to 0.35fs. Beyond this frequency, the “direct” curve is quite noisy. The parameter values obtained are presented in Table 4

Table 4. Obtained parameters values for large defocus

table-icon
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.

In this case, the minimization enables to well distinguish between α and defocus Δ. The table shows a small overestimation of α and a small underestimation of the MTF (less than 0.01 at Nyquist frequency). For an ideal artificial edge target, it is possible, at least in the present Pleiades case, to measure the MTF and the defocus simultaneously. The obtained accuracies are respectively better than 0.01 for the MTF and smaller than 15 µm for the defocus.

Unlike expected, it should not be possible to use an ordinary image of the target. The instrument has to be widely defocused to obtain an appropriate image of the target.

Although less easy to do, this does not prevent from using this method in orbit. Some work remains to do: a measurement accuracy assessment in the case of a real artificial target such as Salon-de-Provence target and an increase of the treated cases.

9. Conclusion

The edge method has been improved and this improvement has enlarged the application domain of the method. The use of the symmetry enables to manage with poor quality edges. The insertion of a parametric transfer function model offers many advantages: noise cut, oversampling rate optimization and potential defocus assessment. Promising results have been obtained mainly for SPOT 5 and Pleiades. Foreseen work concerns Pleiades with a test of the method on images of a real artificial target such as the Salon-de-Provence checkerboard. This should be possible using airborne acquisitions of the Salon-de-Provence target as landscape input of the simulations. Another work to do is to estimate for the Pleiades optical combination how representative the transfer function model is. Improvement of the transfer function model could be done concerning the central obscuration. The behavior of the method for the defocus assessment should also be tested for more classical MTF and SNR such as SPOT 5 ones.

Acknowledgements

We wish to acknowledge CNES for giving us the authorization to use the SPOT 1 La Crau image and for the Pleiades simulations. Special thanks to Mr Philippe Kubik for his simulated images and his fruitful discussions.

References and links

1.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983). [CrossRef]

2.

W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

3.

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987). [CrossRef]

4.

T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).

5.

H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

6.

H. Hwang, Y.-W. Choi, S. Kwak, M. Kim, and W. Park, “MTF assessment of high resolution satellite images using ISO 12233 slanted-edge method”, Proc. SPIE 7109, 710905–1-710905–9 (2008).

7.

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

8.

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998). [CrossRef]

9.

D. Léger, F. Viallefont, P. Déliot, and C. Valorge, “On-orbit MTF assessment of satellite cameras”, in Post-launch calibration of satellite sensors, Morain and Budge, ed. (Taylor and Francis group, London, 2004).

10.

W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).

11.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003). [CrossRef]

12.

A. Rosak, C. Latry, V. Pascal, and D. Laubier, “From SPOT5 to Pleiades-HR: evolutions of the instrumental specifications”, in Proceedings of the 5th international conference on Space Optics, B. Warmbein, ed. (ESA SP-554, Noordwijk, Netherlands, 2004), 141–148.

OCIS Codes
(110.3000) Imaging systems : Image quality assessment
(110.4100) Imaging systems : Modulation transfer function
(280.0280) Remote sensing and sensors : Remote sensing and sensors

ToC Category:
Imaging Systems

History
Original Manuscript: October 6, 2009
Revised Manuscript: November 12, 2009
Manuscript Accepted: November 30, 2009
Published: February 3, 2010

Citation
Françoise Viallefont-Robinet and Dominique Léger, "Improvement of the edge method for on-orbit MTF measurement," Opt. Express 18, 3531-3545 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3531


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References

  1. M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983). [CrossRef]
  2. W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).
  3. K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987). [CrossRef]
  4. T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).
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