Abstract

For an optical imaging system, the critical output is the image itself, and therefore, the quality of that image is of utmost importance. To estimate or predict the image quality (IQ), a simulation/model is typically created to yield an output image, given an imaging system and an object/scene. The IQ is typically graded based on the imaging system along with the scene. Developing an imaging simulation and creating input scenes to produce IQ results can be time-consuming, leading to a desire for a simple method to estimate the predicted IQ. This work develops a national image interpretability rating scale (NIIRS) IQ value based on simplifying assumptions for remote-sensing purposes. While the results are on the optimistic side, this back-of-the-envelope IQ estimation allows the process of developing a new imaging system to move forward more in parallel rather than in series, i.e., developing an imaging full simulation/model in parallel with designing/procuring hardware.

© 2019 Optical Society of America

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References

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  1. J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Imaging Systems: Modeling and Performance Prediction (Artech House, 2001).
  2. J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, and N. Salvaggio, “General image-quality equation: GIQE,” Appl. Opt. 36, 8322–8328 (1997).
    [Crossref]
  3. S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
    [Crossref]
  4. R. D. Fiete, Modeling the Imaging Chain of Digital Cameras (SPIE, 2010).
  5. J. E. Greivenkamp, Field Guide to Geometric Optics, Vol. FG01 of SPIE Field Guides (SPIE, 2004).
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  7. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986), pp. 130–131.
  8. J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, and N. Salvaggio, “General image-quality equation for infrared imagery,” Appl. Opt. 39, 4826–4828 (2000).
    [Crossref]
  9. M. T. Eismann and S. D. Ingle, Utility Analysis of High-Resolution Multispectral Imagery (Environmental Research Institute of Michigan, 1995), Vol. 3, p. 36.

2008 (1)

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[Crossref]

2000 (1)

1997 (1)

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986), pp. 130–131.

Colburn, L.

Driggers, R. G.

J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Imaging Systems: Modeling and Performance Prediction (Artech House, 2001).

Eismann, M. T.

M. T. Eismann and S. D. Ingle, Utility Analysis of High-Resolution Multispectral Imagery (Environmental Research Institute of Michigan, 1995), Vol. 3, p. 36.

Fienup, J. R.

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[Crossref]

Fiete, R. D.

R. D. Fiete, Modeling the Imaging Chain of Digital Cameras (SPIE, 2010).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Greivenkamp, J. E.

J. E. Greivenkamp, Field Guide to Geometric Optics, Vol. FG01 of SPIE Field Guides (SPIE, 2004).

Ingle, S. D.

M. T. Eismann and S. D. Ingle, Utility Analysis of High-Resolution Multispectral Imagery (Environmental Research Institute of Michigan, 1995), Vol. 3, p. 36.

Irvine, J.

Leachtenauer, J. C.

Malila, W.

Salvaggio, N.

Thurman, S. T.

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[Crossref]

Appl. Opt. (2)

Proc. SPIE (1)

S. T. Thurman and J. R. Fienup, “Analysis of the general image quality equation,” Proc. SPIE 6978, 69780F (2008).
[Crossref]

Other (6)

R. D. Fiete, Modeling the Imaging Chain of Digital Cameras (SPIE, 2010).

J. E. Greivenkamp, Field Guide to Geometric Optics, Vol. FG01 of SPIE Field Guides (SPIE, 2004).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986), pp. 130–131.

M. T. Eismann and S. D. Ingle, Utility Analysis of High-Resolution Multispectral Imagery (Environmental Research Institute of Michigan, 1995), Vol. 3, p. 36.

J. C. Leachtenauer and R. G. Driggers, Surveillance and Reconnaissance Imaging Systems: Modeling and Performance Prediction (Artech House, 2001).

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Figures (7)

Fig. 1.
Fig. 1. Simplified imaging system and object/scene (Lambertian).
Fig. 2.
Fig. 2. GSD plotted as a function of the imaging system’s f/#. The GSD is monotonically decreasing in f/#.
Fig. 3.
Fig. 3. Imaging system’s RER as a function of f/#. The RER is monotonically decreasing in f/# between zero and one.
Fig. 4.
Fig. 4. SNR as a function of the imaging system’s f/# as defined in Refs. [1,2]. The SNR is monotonically decreasing in f/#.
Fig. 5.
Fig. 5. Composite NIIRS score shown as a function of the imaging system’s f/#. For this system, the optimum or peak NIIRS value is 4.1 for an f/ 15 (or focal length of 3.75 m).
Fig. 6.
Fig. 6. NIIRS as a function of the imaging system’s f/pp. NIIRS value at 4.1 gives an optimum f/pp of 950,000.
Fig. 7.
Fig. 7. NIIRS as a function of the “Q.” The Q value for a peak NIIRS is 2.2.

Equations (15)

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NIIRS=11.81+3.32log10(0.0254)+3.32log10(RERGSD)1.48HGSNR,
GSD=|1zf|ppzfpp,
SNRπ4QE(r2r1)LAt(f/#)21(π4QE(r2)LAt(f/#)2)+(π4QE(r1)LAt(f/#)2)=π4QELAt(f/#)2(r2r1)r2+r1,
OTF(σ)=1|σ1λf/#|,
O(σ)=F{H(x)}=12(δ(σ)+1jπσ),
I(σ)=OTF(σ)·O(σ)=12(1|σ1λf/#|)(δ(σ)+1jπσ),
i(x)=F1{I(σ)}=12(1+sgn(x)λf/#π2x).
RER=i(pp2)i(pp2)=(12λf/#π2pp).
NIIRS=5.03+3.32log10(12λf/#π2ppzfpp)1π4QELAt(f/#)2·(r2r1)r2+r1,
NIIRS=5.03+3.32log10(fzpp(12λf/Dπ2pp))2f/Dr2+r1πQELt·pp(r2r1),
dNIIRSdf0.
NIIRS=5.03+3.32log10(1z(fpp)(12λ/Dπ2(fpp)))2/Dr2+r1πQELt·(r2r1)(fpp).
RER=(12Qπ2).
NIIRS=10.751+3.32log10(0.0254)+log10(RERaGSDb)1.48H0.344GSNR,
NIIRS=5.455+log10((12λf/Dπ2pp)a(zfpp)b)0.688f/DL2+L1πQEt·pp(L2L1),

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