Abstract

We have recently shown [Appl. Opt. 51, 2739 (2012)] that performance analysis of optical imaging systems based on results obtained with classic one-dimensional (1D) resolution targets (such as the U.S. Air Force resolution target) are significantly different than those obtained with a newly proposed two-dimensional (2D) target. We hereby provide experimental evidence and show how the new 2D template can be used to correctly characterize optical imaging systems in terms of resolution and contrast. In particular, we apply the consequences of these observations to the optimal design of some 2D barcode structures.

© 2012 Optical Society of America

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References

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  1. H. Haim, E. Marom, and N. Konforti, “Optical imaging systems analyzed with a two-dimensional template,” Appl. Opt. 51, 2739–2746 (2012).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 126–151.
  3. G. L. Rogers, “Measurement of the modulation transfer function of paper,” Appl. Opt. 37, 7235–7240 (1998).
    [CrossRef]
  4. A. K. Jaiswal and R. K. Bhogra, “Resolution for a general two bar target,” Appl. Opt. 15, 1911–1912 (1976).
    [CrossRef]
  5. D. N. Sitter, J. S. Goddard, and R. K. Ferrell, “Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns,” Appl. Opt. 34, 746–751 (1995).
    [CrossRef]
  6. G. D. Boreman and S. Yang, “Modulation transfer function measurement using three- and four-bar targets,” Appl. Opt. 34, 8050–8052 (1995).
    [CrossRef]
  7. H. Osterberg, “Evaluation phase optical tests,” in Military Standardization Handbook: Optical Design (Defense Supply Agency, 1962), pp. 1–8.
  8. V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).
  9. J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44, 468–471 (1954).
    [CrossRef]
  10. E. Marom, B. Milgrom, and N. Konforti, “Two-dimensional modulation transfer function: a new perspective,” Appl. Opt. 49, 6749–6755 (2010).
    [CrossRef]
  11. Inlite, “ClearImage Free Online Barcode Reader” http://online-barcode-reader.inliteresearch.com/default.aspx .

2012 (1)

2010 (1)

1998 (1)

1995 (2)

1976 (1)

1954 (1)

1923 (1)

V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).

Bhogra, R. K.

Boreman, G. D.

Coltman, J. W.

Ferrell, R. K.

Goddard, J. S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 126–151.

Haim, H.

Jaiswal, A. K.

Konforti, N.

Marom, E.

Milgrom, B.

Osterberg, H.

H. Osterberg, “Evaluation phase optical tests,” in Military Standardization Handbook: Optical Design (Defense Supply Agency, 1962), pp. 1–8.

Rogers, G. L.

Ronchi, V.

V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).

Sitter, D. N.

Yang, S.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] (1)

V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 126–151.

H. Osterberg, “Evaluation phase optical tests,” in Military Standardization Handbook: Optical Design (Defense Supply Agency, 1962), pp. 1–8.

Inlite, “ClearImage Free Online Barcode Reader” http://online-barcode-reader.inliteresearch.com/default.aspx .

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Figures (10)

Fig. 1.
Fig. 1.

Typical target element of (a) the Air Force resolution target and (b) the proposed 2D checkerboard element. Note that cell size is identical in (a) and (b).

Fig. 2.
Fig. 2.

The system response to two-and four-point input. (a) and (b) show the input target (left) and the output (right) for f=fc/2. (c) and (d) show a cross section along the center of input and output cells of (a) and (b) respectively. (e) and (d) show the input target (left) and output (right) for f=fc/2, with their cross sections in (g) and (h), respectively.

Fig. 3.
Fig. 3.

Geometrical properties of the chess-bar target.

Fig. 4.
Fig. 4.

The chess-bar template.

Fig. 5.
Fig. 5.

The chess-bar target (upper center) can be segmented into a 2D structure (left) and 1D structures (right and bottom).

Fig. 6.
Fig. 6.

Simulation process comparing the chess-bar target with the 2D target. Imaging simulation performed on the two inputs produced the two output images on the top. The bottom image shows the cross section along the center line of the two outputs.

Fig. 7.
Fig. 7.

Chess-bar target after imaging (left) and after image enhancement by histogram equalization (right).

Fig. 8.
Fig. 8.

The contrast was calculated by searching for the minimum value in the dark region (red circle) and the average of the peak value in the two or four bright regions (blue square) for the cropped 1D and 2D sectors, respectively.

Fig. 9.
Fig. 9.

CTF of 1D (upper image) and 2D (lower image) targets. Both plots contain the simulation and theoretical result along the experimental results.

Fig. 10.
Fig. 10.

PDF417 barcode with aspect ratio of 31 (upper image) and 11 (lower image) containing the first sentence of the Gettysburg address.

Tables (2)

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Table 1. Minimal Magnifying Factor M Necessary for Achieving Deciphering

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Table 2. Minimum Magnification Factor M as a Function of the Aspect Ratio of PDF417 Barcodes

Equations (9)

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

OTF(fx,fy)=P(x+λzifx2,y+λzify2)·P*(xλzifx2,yλzify2)dxdy|P(x,y)|2dxdy,
MTF(f)={2π[arccos(ffc)ffc·1(ffc)2]ffc0otherwise,
Ssqw(x)=12(1+4πn=1,3,5sin(nπxa)n),
Ssqwout(x)=12(1+4πn=1,3,5sin(nπxa)n·MTF(n2a)).
Schecker(x,y)=12(1+(4π)2n=1,3,5sin(nπxa)nn=1,3,5sin(mπya)m).
Scheckerout(x,y)=12(1+(4π)2n=1,3,5m=1,3,5sin(nπxa)n·sin(mπya)m·MTF(n2+m22a)).
MTF(2/2a)=0fc=2/2a=2·f,
Area(11)Area(13)·100%=1.7423·1.22·100%=70.1%.
Area(11)Area(13)·100%=1.823·1.22·100%=75%.

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