Abstract

We show theoretically and verify experimentally that the modulation transfer function (MTF) of a printing system can be determined by measuring the autocorrelation of a printed Ronchi grating. In practice, two similar Ronchi gratings are printed on two transparencies and the transparencies are superimposed with parallel grating lines. Then, the gratings are uniformly illuminated and the transmitted light from a large section is measured versus the displacement of one grating with respect to the other in a grating pitch interval. This measurement provides the required autocorrelation function for determination of the MTF.

© 2009 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  2. G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD, 1993).
  3. K. Murata, “Instruments for the measuring of optical transfer function,” Prog. Opt. 5, 199-245 (1966).
    [CrossRef]
  4. C. S. Williams, Introduction to the Optical Transfer Function (Wiley, 1989).
  5. L. R. Baker, ed., Selected Papers on Optical Transfer Function: Measurement, Vol. MS60 of SPIE Milestone Series (SPIE Press, 1992).
  6. V. Havránek, “Overview of OTF measurement,” Acta Univ. Palacki. Olomuc. Fac. Rer. Nat., Physica 40-41, 63-86 (2001-2002).
  7. C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).
  8. C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).
  9. J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.
  10. S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).
  11. K. Madanipour and M. T. Tavassoly, “Application of moiré technique to the measurement of modulation transfer functions (MTF) of printing systems,” Opt. Lasers Eng. 45, 64-69(2007).
    [CrossRef]
  12. J. W. Coltman, “The Specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44, 468-471(1954).
    [CrossRef]
  13. S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
    [CrossRef]
  14. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
    [CrossRef]

2007 (1)

K. Madanipour and M. T. Tavassoly, “Application of moiré technique to the measurement of modulation transfer functions (MTF) of printing systems,” Opt. Lasers Eng. 45, 64-69(2007).
[CrossRef]

2006 (1)

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
[CrossRef]

2002 (1)

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

2001 (1)

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

2000 (1)

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

1966 (1)

K. Murata, “Instruments for the measuring of optical transfer function,” Prog. Opt. 5, 199-245 (1966).
[CrossRef]

1954 (1)

Anderson, P. G.

J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.

Arney, J. S.

J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.

Ayer, K.

J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Coltman, J. W.

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
[CrossRef]

Fujino, M.

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

Havránek, V.

V. Havránek, “Overview of OTF measurement,” Acta Univ. Palacki. Olomuc. Fac. Rer. Nat., Physica 40-41, 63-86 (2001-2002).

Holst, G. C.

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD, 1993).

Inoue, S.

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

Koopipat, C.

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

Madanipour, K.

K. Madanipour and M. T. Tavassoly, “Application of moiré technique to the measurement of modulation transfer functions (MTF) of printing systems,” Opt. Lasers Eng. 45, 64-69(2007).
[CrossRef]

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Mehta, P.

J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.

Miake, Y.

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

Miyake, Y.

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

Miyata, K.

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

Murata, K.

K. Murata, “Instruments for the measuring of optical transfer function,” Prog. Opt. 5, 199-245 (1966).
[CrossRef]

Parrent, G. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
[CrossRef]

Rasouli, S.

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
[CrossRef]

Tavassoly, M. T.

K. Madanipour and M. T. Tavassoly, “Application of moiré technique to the measurement of modulation transfer functions (MTF) of printing systems,” Opt. Lasers Eng. 45, 64-69(2007).
[CrossRef]

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Thompson, B. J.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
[CrossRef]

Tsumura, N.

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

Williams, C. S.

C. S. Williams, Introduction to the Optical Transfer Function (Wiley, 1989).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Yamazaki, S.

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

J. Imaging Sci. Technol. (3)

C. Koopipat, N. Tsumura, Y. Miyake, and M. Fujino, “Effect of ink spread and optical dot gain on the MTF of ink jet image,” J. Imaging Sci. Technol. 46, 321-325 (2002).

C. Koopipat, N. Tsumura, M. Fujino, K. Miyata, and Y. Miake, “Image evaluation and analysis of ink jet printing system (I): MTF measurement and analysis of ink jet images,” J. Imaging Sci. Technol. 45, 591-597 (2001).

S. Inoue, S. Yamazaki, N. Tsumura, and K. Miyata, “An evaluation of image quality for hard copy based on the MTF of paper,” J. Imaging Sci. Technol. 44, 188-195 (2000).

J. Opt. Soc. Am. (1)

Opt. Lasers Eng. (1)

K. Madanipour and M. T. Tavassoly, “Application of moiré technique to the measurement of modulation transfer functions (MTF) of printing systems,” Opt. Lasers Eng. 45, 64-69(2007).
[CrossRef]

Proc. SPIE (1)

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function (MTF) of the atmosphere in the surface layer by moiré technique,” Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Prog. Opt. (1)

K. Murata, “Instruments for the measuring of optical transfer function,” Prog. Opt. 5, 199-245 (1966).
[CrossRef]

Other (7)

C. S. Williams, Introduction to the Optical Transfer Function (Wiley, 1989).

L. R. Baker, ed., Selected Papers on Optical Transfer Function: Measurement, Vol. MS60 of SPIE Milestone Series (SPIE Press, 1992).

V. Havránek, “Overview of OTF measurement,” Acta Univ. Palacki. Olomuc. Fac. Rer. Nat., Physica 40-41, 63-86 (2001-2002).

J. S. Arney, P. G. Anderson, P. Mehta, and K. Ayer, “The MTF of printing systems,” Proceedings of NIP16: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, 2000), pp. 367-369.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD, 1993).

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, 1989), pp. 433-444.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for measuring the autocorrelation function: S, illuminating source; L1, collimating lens; L2, condenser lens; G1 and G2, gratings; and PD, photodetector.

Fig. 2
Fig. 2

Experimental setup to measure the ACTF of gratings: S, illuminating source; SL, adjustable slit; L1, collimating lens; L2, condenser lens; G1 and G2, gratings; g1 and g2, supporting glasses; W, square window; PD, photodetector; Amp, amplifier; A/D, analog-to-digital converter; COM, computer; and Scan, scanner with 0.1 μm displacement precision.

Fig. 3
Fig. 3

Output of the detector versus relative displacement of a pair of gratings that is proportional to the ACTF.

Fig. 4
Fig. 4

ACTF of the Ronchi gratings with d = 0.5925 mm ; the triangle represents the autocorrelation function of ideal Ronchi gratings.

Fig. 5
Fig. 5

MTF of the HP1200 laser printer evaluated by measuring the ACTF of different Ronchi gratings by the first setup.

Fig. 6
Fig. 6

MTF of the HP1200 laser printer evaluated by measuring the ACTF of different Ronchi gratings by the second setup.

Equations (12)

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t ( x ) = n = + a n OTF ( n d ) exp ( i 2 π n x d ) ,
C ( x ) = t * ( x ) t ( x + x ) lim L 1 L L 2 + L 2 t * ( x ) t ( x + x ) d x .
V ( x ) = β I 0 C ( x ) ,
V ( x ) = β I 0 [ n , m = + a n * a m OTF * ( n d ) OTF ( m d ) exp ( i 2 π m x d ) lim L 1 L L 2 L 2 exp ( i 2 π x ( m n ) d ) d x ] ,
V ( x ) = β I 0 [ n = + a n 2 MTF 2 ( n d ) exp ( i 2 π n x d ) ] ,
V ( x ) = β I 0 [ a 0 2 + 2 n = 1 a n 2 MTF 2 ( n d ) cos ( 2 π n x d ) ] .
V Max = β I 0 [ a 0 2 + 2 n = 1 a n 2 MTF 2 ( n d ) ] ,
V Min = β I 0 [ a 0 2 2 n = 1 a n 2 MTF 2 ( n d ) ] .
β I 0 = 2 ( V Max + V Min ) .
C ( x ) = V ( x ) 2 ( V Max + V Min ) ,
C ( x ) = [ a 0 2 + 2 n = 1 a n 2 MTF 2 ( n d ) cos ( 2 π n x d ) ] .
MTF ( n d ) = [ 1 a n 2 d d 2 d 2 C ( x ) cos ( 2 π n x d ) d x ] 1 2 .

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