Abstract

The point-spread function (PSF) of a camera can seriously affect the accuracy of radiometric calibration and measurement. We found that the PSF can produce a 3.7% difference between the apparent measured radiance of two plaques of different sizes with the same illumination. This difference can be removed by deconvolution with the measured PSF. To determine the PSF, many images of a collimated beam from a He-Ne laser are averaged. Since our optical system is focused at infinity, it should focus this source to a single pixel. Although the measured PSF is very sharp, dropping 4 and 6 orders of magnitude and 8 and 100 pixels away from the point source, respectively, we show that the effect of the PSF as far as 100 pixels away cannot be ignored without introducing an appreciable error to the calibration. We believe that the PSF should be taken into account in all optical systems to obtain accurate radiometric measurements.

© 2004 Optical Society of America

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References

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  1. C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
    [CrossRef]
  2. J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
    [CrossRef]
  3. J. R. G. Townshend, “The spatial resolving power of earth resources satellites,” Prog. Phys. Geog. 5, 32–55 (1981).
    [CrossRef]
  4. S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
    [CrossRef]
  5. R. A. Schowengerdt, Remote Sensing (Academic, San Diego, Calif., 1997).
  6. H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
    [CrossRef]
  7. S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
    [CrossRef]
  8. J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
    [CrossRef]
  9. J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
    [CrossRef]
  10. N. H. Nakashima, A. W. S. Johnson, “Measuring the PSF from aperture images of arbitrary shape-an algorithm,” Ultramicroscopy 94, 135–148 (2003).
    [CrossRef]
  11. B. L. Markham, “The Landsat sensors’ spatial responses,” IEEE Trans. Geosci. Remote Sens. 23, 864–875 (1985).
    [CrossRef]
  12. A. P. Cracknell, “Synergy in remote sensing-what’s in a pixel,” Int. J. Remote Sens. 19, 2025–2047 (1998).
    [CrossRef]

2003

N. H. Nakashima, A. W. S. Johnson, “Measuring the PSF from aperture images of arbitrary shape-an algorithm,” Ultramicroscopy 94, 135–148 (2003).
[CrossRef]

2002

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
[CrossRef]

2000

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

1999

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

1998

J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
[CrossRef]

A. P. Cracknell, “Synergy in remote sensing-what’s in a pixel,” Int. J. Remote Sens. 19, 2025–2047 (1998).
[CrossRef]

1997

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

1985

B. L. Markham, “The Landsat sensors’ spatial responses,” IEEE Trans. Geosci. Remote Sens. 23, 864–875 (1985).
[CrossRef]

1981

J. R. G. Townshend, “The spatial resolving power of earth resources satellites,” Prog. Phys. Geog. 5, 32–55 (1981).
[CrossRef]

Bell, J. F.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Chassery, J. M.

J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
[CrossRef]

Clark, B.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Cracknell, A. P.

A. P. Cracknell, “Synergy in remote sensing-what’s in a pixel,” Int. J. Remote Sens. 19, 2025–2047 (1998).
[CrossRef]

Darlington, E. H.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

DeFries, R. S.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

Godden, G.

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

Gold, R.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Guenther, B.

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

Harch, A.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Hawkins, S. E.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Helfenstein, P.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Heyler, G.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Huang, C.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

Izenberg, N.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Johnson, A. W. S.

N. H. Nakashima, A. W. S. Johnson, “Measuring the PSF from aperture images of arbitrary shape-an algorithm,” Ultramicroscopy 94, 135–148 (2003).
[CrossRef]

Kalluri, S. N.

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

Kalluri, S. N. V.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

Keeney, A.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Lehr, J.

J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
[CrossRef]

Li, H.

H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
[CrossRef]

Liang, S.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

Markham, B. L.

B. L. Markham, “The Landsat sensors’ spatial responses,” IEEE Trans. Geosci. Remote Sens. 23, 864–875 (1985).
[CrossRef]

Merline, W.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Murchie, S.

H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
[CrossRef]

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Murphy, P.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Nakashima, N. H.

N. H. Nakashima, A. W. S. Johnson, “Measuring the PSF from aperture images of arbitrary shape-an algorithm,” Ultramicroscopy 94, 135–148 (2003).
[CrossRef]

Owen, W.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Peacock, K.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Pycock, D.

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

Qiu, S.

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

Quigley, S.

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

Robinson, M.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Robinson, M. S.

H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
[CrossRef]

Schowengerdt, R. A.

R. A. Schowengerdt, Remote Sensing (Academic, San Diego, Calif., 1997).

Sibarita, J. B.

J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
[CrossRef]

Thomas, P.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Townshend, J. R. G.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

J. R. G. Townshend, “The spatial resolving power of earth resources satellites,” Prog. Phys. Geog. 5, 32–55 (1981).
[CrossRef]

Veverka, J.

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

Wang, X.

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

Webb, P.

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

Yang, K.

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

Zandhuis, J.

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

Icarus

H. Li, M. S. Robinson, S. Murchie, “Preliminary remediation of scattered light in NEAR MSI images,” Icarus 155, 244–252 (2002).
[CrossRef]

S. Murchie, M. Robinson, S. E. Hawkins, A. Harch, P. Helfenstein, P. Thomas, K. Peacock, W. Owen, G. Heyler, P. Murphy, E. H. Darlington, A. Keeney, R. Gold, B. Clark, N. Izenberg, J. F. Bell, W. Merline, J. Veverka, “Inflight calibration of the NEAR Multispectral Imager,” Icarus 140, 66–91 (1999).
[CrossRef]

IEE Proceedings. Vision Image Signal Process.

J. Zandhuis, D. Pycock, S. Quigley, P. Webb, “Sub-pixel nonparametric PSF estimation for image enhancement,” IEE Proceedings. Vision Image Signal Process. 144, 285–292 (1997).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

B. L. Markham, “The Landsat sensors’ spatial responses,” IEEE Trans. Geosci. Remote Sens. 23, 864–875 (1985).
[CrossRef]

IEEE Trans. Image Process.

J. Lehr, J. B. Sibarita, J. M. Chassery, “Image restoration in x-ray microscopy: PSF determination and biological applications,” IEEE Trans. Image Process. 7, 258–263 (1998).
[CrossRef]

Int. J. Remote Sens.

J. R. G. Townshend, C. Huang, S. N. Kalluri, R. S. DeFries, S. Liang, K. Yang, “Beware of per-pixel characterization of land cover,” Int. J. Remote Sens. 21, 839–843 (2000).
[CrossRef]

A. P. Cracknell, “Synergy in remote sensing-what’s in a pixel,” Int. J. Remote Sens. 19, 2025–2047 (1998).
[CrossRef]

Metrologia

S. Qiu, G. Godden, X. Wang, B. Guenther, “Satellite-Earth remote sensor scatter effects on Earth scene radiometric accuracy,” Metrologia 37, 411–414 (2000).
[CrossRef]

Prog. Phys. Geog.

J. R. G. Townshend, “The spatial resolving power of earth resources satellites,” Prog. Phys. Geog. 5, 32–55 (1981).
[CrossRef]

Remote Sens. Environ.

C. Huang, J. R. G. Townshend, S. Liang, S. N. V. Kalluri, R. S. DeFries, “Impact of sensor’s point spread function on land cover characterization: assessment and deconvolution,” Remote Sens. Environ. 80, 203–212 (2002).
[CrossRef]

Ultramicroscopy

N. H. Nakashima, A. W. S. Johnson, “Measuring the PSF from aperture images of arbitrary shape-an algorithm,” Ultramicroscopy 94, 135–148 (2003).
[CrossRef]

Other

R. A. Schowengerdt, Remote Sensing (Academic, San Diego, Calif., 1997).

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Figures (2)

Fig. 1
Fig. 1

PSF measured at exposures of 0.02 and 0.08 s (radial average scaled to 0.01 s of exposure time). Also shown is the fitted PSF with C 1 = 40 and C 2 = 0.3 by use of Eq. (3).

Fig. 2
Fig. 2

Radial average of a circular area source generated by diffusing the expanded He-Ne laser beam. Also shown is a fit to the PSF with C 1 = 3600 and C 2 = 0.3.

Tables (3)

Tables Icon

Table 1 First Six Points of Measured and Normalized PSFs

Tables Icon

Table 2 Sum of PSF (Not Normalized) versus Summation Limit R

Tables Icon

Table 3 Calculated Center Brightness versus Size of Square Plaques of Unit Radiance

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

σdrDN2πrdr1/2
σPrMrN2πrdr1/2,
PSFr=C1 exp-C2rr
PˆSFr=PSFrx=-RRy=-RR PSFx2+y21/2.
PˆSFr>5=6.206×10-4 exp-0.3rr.
Lx, y=IFTFTimagex, y/FTPˆSFx, y.
PSFx, y=PSFmodx+M/2, M-M/22+mody+M/2, M-M/221/2,

Metrics