Abstract

The measurement of a two-dimensional spatial responsivity map of infrared antennas can be accomplished by use of an iterative deconvolution algorithm. The inputs of this algorithm are the spatial distribution of the laser beam irradiance illuminating the antenna-coupled detector and a map of the measured detector response as it moves through the illuminating beam. The beam irradiance distribution is obtained from knife-edge measurements of the beam waist region; this data set is fitted to a model of the beam. The uncertainties, errors, and artifacts of the measurement procedure are analyzed by principal-component analysis. This study has made it possible to refine the measurement protocol and to identify, classify, and filter undesirable sources of noise. The iterative deconvolution algorithm stops when a well-defined threshold is reached. Spatial maps of mean values and uncertainties have been obtained for the beam irradiance distribution, the scanned spatial response data, and the resultant spatial responsivity of the infrared antenna. Signal-to-noise ratios have been defined and compared, and the beam irradiance distribution characterization has been identified as the statistically weakest part of the measurement procedure.

© 2005 Optical Society of America

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References

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  1. C. Fumeaux, G. Boreman, W. Herrmann, F. Kneubühl, H. Rothuizen, “Spatial impulse response of lithographic infrared antennas,” Appl. Opt. 38, 37–46 (1999).
    [CrossRef]
  2. J. Alda, C. Fumeaux, I. Codreanu, J. Schaefer, G. Boreman, “A deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas,” Appl. Opt. 38, 3993–4000 (1999).
    [CrossRef]
  3. I. Codreanu, G. D. Boreman, “Integration of microbolometers with infrared microstrip antennas,” Infrared Phys. Technol. 43, 335–344 (2002).
    [CrossRef]
  4. F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
    [CrossRef]
  5. J. M. López-Alonso, B. Monacelli, G. D. Boreman, “Infrared laser beam temporal fluctuations: characterization and filtering,” Opt. Eng. (to be published).
  6. J. M. López-Alonso, J. Alda, E. Bemabéu, “Principal components characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
    [CrossRef]
  7. J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital-image-acquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
    [CrossRef]
  8. J. M. López-Alonso, J. Alda, “Correlation in finance: a statistical approach,” in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, ed., Proc. SPIE5471, 311–321 (2004).
    [CrossRef]
  9. J. M. López-Alonso, J. Alda “Characterization of dynamic sea scenarios with infrared imagers” Infrared Phys. Technol. 46, 355–363 (2005).
    [CrossRef]
  10. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurements (International Organization for Standarization, 1993).
  11. D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.
  12. C. Fumeaux, J. Alda, G. D. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629–1631, (1999).
    [CrossRef]
  13. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
    [CrossRef]
  14. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
    [CrossRef]

2005 (1)

J. M. López-Alonso, J. Alda “Characterization of dynamic sea scenarios with infrared imagers” Infrared Phys. Technol. 46, 355–363 (2005).
[CrossRef]

2004 (1)

J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital-image-acquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[CrossRef]

2002 (3)

I. Codreanu, G. D. Boreman, “Integration of microbolometers with infrared microstrip antennas,” Infrared Phys. Technol. 43, 335–344 (2002).
[CrossRef]

F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
[CrossRef]

J. M. López-Alonso, J. Alda, E. Bemabéu, “Principal components characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[CrossRef]

1999 (3)

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

1972 (1)

Alda, J.

J. M. López-Alonso, J. Alda “Characterization of dynamic sea scenarios with infrared imagers” Infrared Phys. Technol. 46, 355–363 (2005).
[CrossRef]

J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital-image-acquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[CrossRef]

J. M. López-Alonso, J. Alda, E. Bemabéu, “Principal components characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[CrossRef]

C. Fumeaux, J. Alda, G. D. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629–1631, (1999).
[CrossRef]

J. Alda, C. Fumeaux, I. Codreanu, J. Schaefer, G. Boreman, “A deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas,” Appl. Opt. 38, 3993–4000 (1999).
[CrossRef]

J. M. López-Alonso, J. Alda, “Correlation in finance: a statistical approach,” in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, ed., Proc. SPIE5471, 311–321 (2004).
[CrossRef]

Bemabéu, E.

Boreman, G.

Boreman, G. D.

I. Codreanu, G. D. Boreman, “Integration of microbolometers with infrared microstrip antennas,” Infrared Phys. Technol. 43, 335–344 (2002).
[CrossRef]

F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
[CrossRef]

C. Fumeaux, J. Alda, G. D. Boreman, “Lithographic antennas at visible frequencies,” Opt. Lett. 24, 1629–1631, (1999).
[CrossRef]

J. M. López-Alonso, B. Monacelli, G. D. Boreman, “Infrared laser beam temporal fluctuations: characterization and filtering,” Opt. Eng. (to be published).

Codreanu, I.

Fumeaux, C.

Gonzalez, F. J.

F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
[CrossRef]

Gritz, M. A.

F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
[CrossRef]

Herrmann, W.

Kneubühl, F.

López-Alonso, J. M.

J. M. López-Alonso, J. Alda “Characterization of dynamic sea scenarios with infrared imagers” Infrared Phys. Technol. 46, 355–363 (2005).
[CrossRef]

J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital-image-acquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[CrossRef]

J. M. López-Alonso, J. Alda, E. Bemabéu, “Principal components characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[CrossRef]

J. M. López-Alonso, J. Alda, “Correlation in finance: a statistical approach,” in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, ed., Proc. SPIE5471, 311–321 (2004).
[CrossRef]

J. M. López-Alonso, B. Monacelli, G. D. Boreman, “Infrared laser beam temporal fluctuations: characterization and filtering,” Opt. Eng. (to be published).

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

Monacelli, B.

J. M. López-Alonso, B. Monacelli, G. D. Boreman, “Infrared laser beam temporal fluctuations: characterization and filtering,” Opt. Eng. (to be published).

Morrison, D. F.

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

Richardson, W. H.

Rothuizen, H.

Schaefer, J.

Appl. Opt. (3)

Astron. J. (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

Infrared Phys. Technol. (2)

J. M. López-Alonso, J. Alda “Characterization of dynamic sea scenarios with infrared imagers” Infrared Phys. Technol. 46, 355–363 (2005).
[CrossRef]

I. Codreanu, G. D. Boreman, “Integration of microbolometers with infrared microstrip antennas,” Infrared Phys. Technol. 43, 335–344 (2002).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

F. J. Gonzalez, M. A. Gritz, C. Fumeaux, G. D. Boreman, “Two dimensional array of antenna-coupled microbolometers,” Int. J. Infrared Millim. Waves 23, 785–797 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital-image-acquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[CrossRef]

Opt. Lett. (1)

Other (4)

J. M. López-Alonso, J. Alda, “Correlation in finance: a statistical approach,” in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, ed., Proc. SPIE5471, 311–321 (2004).
[CrossRef]

International Organization for Standardization, Guide to the Expression of Uncertainty in Measurements (International Organization for Standarization, 1993).

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

J. M. López-Alonso, B. Monacelli, G. D. Boreman, “Infrared laser beam temporal fluctuations: characterization and filtering,” Opt. Eng. (to be published).

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Figures (11)

Fig. 1
Fig. 1

Flowchart of the measurement procedure, highlighting the steps in which the PCA method is applied.

Fig. 2
Fig. 2

Top, Knife scan original data after differentiation with respect to the scan coordinate (along the vertical axis); Horizontal axis, axis of beam propagation. Center, Eigenvalues and their uncertainties obtained after the PCA method is applied to the original data set. Bottom, filtered data set removal of random noise that corresponds to a principal-component group from Y4 to Y100.

Fig. 3
Fig. 3

Evolution of the first-order and second-order moments for the horizontal and vertical filtered knife-edge data. The plots of the first-order moment show a residual misalignment of the optical train. This misalignment is ~2.8° for the horizontal axis and ~4.2° for the vertical axis.

Fig. 4
Fig. 4

Top, filtered knife-edge data for the horizontal (left) and vertical (right) directions. After the beam waist location and depth are defined it is possible to obtain the averaged beam profiles (center) and their uncertainties (bottom).

Fig. 5
Fig. 5

PCA applied to the modeled beam irradiance distribution. The original distributions are generated by fitting of the modeled beam with the data obtained for the beam waist region after a collection of knife-edge profiles is generated that takes into account the uncertainties of the data. The general spatial structure of the beam is explained by Y1Y14. The rest of the principal components (PCs) are related to numerical noise introduced by the fitting algorithm and therefore can be filtered out.

Fig. 6
Fig. 6

Mean irradiance distribution (left, top) and its standard deviation (STD; right, top). The SNR map is obtained after division of the previous two maps (left, bottom). Representing the SNR for all the points yields the figure at bottom right. Fitting these points to a linear function yields a global SNRbeam.

Fig. 7
Fig. 7

Images that correspond to principal components Y1, Y2, Y3, Y4, and Y5 obtained from a collection of nine experimental 2D scan maps (left) column from upper to lower). These scan sets are not centered. Center, original 2D scan maps #1 and #9. The difference between these maps reveals the effect of decentering the data. This subtraction image resembles the Y2 map, again illustrating the filtering power of PCA.

Fig. 8
Fig. 8

Top, eigenvalues for decentered and centered data. Bottom, evolution of the location of the data center in the XY plane.

Fig. 9
Fig. 9

The PCA method applied to the centered data provides a first principal component Y1 (top), which is the same as that obtained from the original data, and a second principal component Y2, which contains information about the effect of the cooling system’s influence on the laser output.

Fig. 10
Fig. 10

Application of the PCA method to the 2D maps permits definition of an averaged map (top left) and a map of its standard deviation (STD; top right). From these two images it is possible to obtain the map of the SNR (bottom left) and a mean value of this parameter SNRscan after the SNR data are fitted with a linear function.

Fig. 11
Fig. 11

Antenna’s spatial response (top left) and its uncertainties [standard deviation (STD), top right]. These maps are obtained after deconvolution of the signals and application of the PCA method to the deconvolved results. Bottom left, spatial structure and value of the SNR. Linear fitting of the individual values of the SNR provides a global SNRrespons value.

Equations (7)

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g = f ( x 1 , , x k , , x N ) .
Y α = k = 1 N e α ( k ) x k ,
Ω α = λ α / α = 1 N λ α
x k = α = 1 N e α ( k ) Y α .
E ( x , y ) = exp ( - x 2 + y 2 ω 0 2 ) ( 2 J 1 ( v ) v - α cos ϕ 2 J 4 ( v ) v - α 2 1 2 v × { J 1 ( v ) 4 - J 3 ( v ) 20 + J 5 ( v ) 4 - 9 J 7 ( v ) 20 - cos 2 ϕ [ 2 J 3 ( v ) 5 + 3 J 7 ( v ) 5 ] } ) ,
v = 2 π λ a z ( x 2 + y 2 ) 1 / 2 ,
ɛ = 1 / SNR .

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