Abstract

In this paper, we use digital holography (DH) in the off-axis image plane recording geometry with a 532 nm continuous-wave laser to measure the system efficiencies (multiplicative losses) associated with a closed-form expression for the signal-to-noise ratio (SNR). Measurements of the mixing efficiency (36.8%) and the reference noise efficiency (74.5%) provide an expected total system efficiency of 22.7%±6.5% and a measured total system efficiency of 21.1%±6.3%. These total noise efficiencies do not include our measurements of the signal noise efficiency (3%–100%), which are highly dependent on the signal strength and become significant for SNRs>100. Thus, the results confirm that the mixing efficiency is generally the dominant multiplicative loss with respect to the DH system under test; however, excess reference and signal noise are significant multiplicative losses as well. Previous results also agree with these experimental findings.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  22. Goodman uses the RMS (or amplitude definition) of SNR and the speckle contrast is the inverse of the SNR (i.e., the standard deviation to the mean). Since we used the power definition of the SNR, C2 enables a better comparison to our measurements.

2019 (1)

2018 (2)

D. E. Thornton, M. F. Spencer, C. A. Rice, and G. P. Perram, “Efficiency measurements for a digital- holography system,” Proc. SPIE 10650, 1065004 (2018).
[Crossref]

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

2016 (1)

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

2011 (1)

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

2009 (1)

1993 (1)

1991 (1)

P. C. D. Hobbs, “Reaching the shot noise limit for $10,” Opt. Photonics News 2(4), 17–23 (1991).
[Crossref]

1983 (1)

1981 (1)

1968 (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[Crossref]

1966 (1)

Banet, M. T.

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Boreman, G. D.

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

Capron, B. A.

Dereniak, E. L.

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

Dundigal, S. R.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Foord, R.

Furth, P. M.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Garimella, A.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

Grow, T. D.

Harney, R. C.

Hobbs, P. C. D.

P. C. D. Hobbs, “Reaching the shot noise limit for $10,” Opt. Photonics News 2(4), 17–23 (1991).
[Crossref]

Höft, T. A.

Janesick, J. R.

J. R. Janesick, Photon Transfer (SPIE, 2007).

Jones, R.

Kendrick, R. L.

Korupolu, R.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Marker, D. K.

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Marron, J. C.

Merritt, P.

P. Merritt and M. F. Spencer, Beam Control for Laser Systems, 2nd ed. (Directed Energy Professional Society, 2018).

Oesch, G. R.

G. R. Oesch, Optical Detection Theory for Laser Applications (Wiley, 2002).

Paschotta, R.

R. Paschotta, “Intensity noise,” in Encyclopedia of Laser Physics and Technology (2008).

Perram, G. P.

Ponnapureddy, V.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Rashid, M. W.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Raynor, R. A.

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Rice, C. A.

D. E. Thornton, M. F. Spencer, C. A. Rice, and G. P. Perram, “Efficiency measurements for a digital- holography system,” Proc. SPIE 10650, 1065004 (2018).
[Crossref]

Schroeder, K. S.

Seldomridge, N.

Shapiro, J. H.

Siegman, A. E.

Spencer, M. F.

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry with comparisons to the self-referencing interferometer,” Appl. Opt. 58, A179–A189 (2019).
[Crossref]

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

D. E. Thornton, M. F. Spencer, C. A. Rice, and G. P. Perram, “Efficiency measurements for a digital- holography system,” Proc. SPIE 10650, 1065004 (2018).
[Crossref]

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

M. F. Spencer, “Spatial heterodyne,” in Encyclopedia of Modern Optics, 2nd ed. (Academic, 2017), Vol. IV, pp. 369–400.

P. Merritt and M. F. Spencer, Beam Control for Laser Systems, 2nd ed. (Directed Energy Professional Society, 2018).

Teich, M. C.

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[Crossref]

Thornton, D. E.

Vaughan, J. M.

Voelz, D. G.

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Willetts, D. V.

Appl. Opt. (5)

IEEE Sens. J. (1)

P. M. Furth, V. Ponnapureddy, S. R. Dundigal, D. G. Voelz, R. Korupolu, A. Garimella, and M. W. Rashid, “Integrated CMOS sensor array for optical heterodyne phase sensing,” IEEE Sens. J. 11, 1516–1521 (2011).
[Crossref]

Opt. Eng. (1)

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opt. Photonics News (1)

P. C. D. Hobbs, “Reaching the shot noise limit for $10,” Opt. Photonics News 2(4), 17–23 (1991).
[Crossref]

Proc. IEEE (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[Crossref]

Proc. SPIE (1)

D. E. Thornton, M. F. Spencer, C. A. Rice, and G. P. Perram, “Efficiency measurements for a digital- holography system,” Proc. SPIE 10650, 1065004 (2018).
[Crossref]

Other (10)

M. F. Spencer, “Spatial heterodyne,” in Encyclopedia of Modern Optics, 2nd ed. (Academic, 2017), Vol. IV, pp. 369–400.

G. R. Oesch, Optical Detection Theory for Laser Applications (Wiley, 2002).

P. Merritt and M. F. Spencer, Beam Control for Laser Systems, 2nd ed. (Directed Energy Professional Society, 2018).

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

J. R. Janesick, Photon Transfer (SPIE, 2007).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

R. Paschotta, “Intensity noise,” in Encyclopedia of Laser Physics and Technology (2008).

FLIR, “How to evaluate camera sensitivity,” https://www.ptgrey.com/white-paper/id/10912 .

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

Goodman uses the RMS (or amplitude definition) of SNR and the speckle contrast is the inverse of the SNR (i.e., the standard deviation to the mean). Since we used the power definition of the SNR, C2 enables a better comparison to our measurements.

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Figures (14)

Fig. 1.
Fig. 1. DH system in the off-axis IPRG. Here, we split the light from the master oscillator (MO) laser into two paths: the illuminator and local oscillator (LO). Given the illuminator, we illuminate an object with an optically rough surface, and we collect the scattered speckle in a pupil given the appropriate receiver optics. Denoted as the signal complex optical field, U S , the pupil focuses the received speckle onto the FPA. In the other path, the LO provides the reference complex optical field, U R , and we inject the LO off axis in the pupil plane at ( x R , y R ) to illuminate the FPA.
Fig. 2.
Fig. 2. Illustration of the demodulation process for a digital hologram. The reference spatially modulates the signal (see the far-left fringes on top of the square image) and the FPA records the digital hologram with noise (i.e., d H + ). Next, we perform an inverse discrete Fourier transform, DF T 1 , on d H + , which produces d ˜ H + in the Fourier plane (magnitude shown). Four terms arise in the Fourier plane: a strong DC term from the reference irradiance (i.e., | A R | 2 ); the autocorrelation of the pupil, U ˜ S ** U ˜ S (centered at DC), which produces a 2D chat profile [14]; the signal complex optical field, U ˜ S (shifted off-axis), since the image and pupil planes are Fourier transform pairs; and the conjugate of the signal complex optical field, U ˜ S * (shifted off-axis in the opposite direction), since the Fourier transform has Hermitian symmetry. We then shift and window the Fourier plane to obtain the estimated signal, U ˜ ^ S , in the pupil plane. Lastly, we perform a discrete Fourier transform, DFT , to obtain the estimated signal, U ^ S , in the image plane (magnitude shown).
Fig. 3.
Fig. 3. Experimental setup for our DH system under test. BD, beam dump; BE, beam expander; FC, fiber coupler; FI, Faraday isolator; λ / 2 , half-wave plate; M, mirror; MO, master oscillator; ND, neutral density filter; PBS, polarizing beam splitter.
Fig. 4.
Fig. 4. Each plot is from dataset 5, where m ¯ S = 96 p e , and represents the full frame. Here, (a) shows a single hologram frame, (b) shows the mean hologram energy in the Fourier plane, (c) shows the mean hologram energy in the image plane E ¯ H ( x , y ) , (d) shows the mean number reference photoelectrons m ¯ R ( x , y ) , (e) shows the mean reference energy in the Fourier plane, (f) shows the mean reference noise energy in the image plane E ¯ R ( x , y ) , (g) shows the mean number signal photoelectrons m ¯ S ( x , y ) , (h) shows the mean signal energy in the Fourier plane, and (i) shows the mean signal noise energy in the image plane E ¯ S ( x , y ) . Note that the first and third columns have square pixels with a rectangular array, which gives rise to rectangular pixels with a square array in the second column.
Fig. 5.
Fig. 5. Azimuthal average of m ¯ S for the six datasets.
Fig. 6.
Fig. 6. Relative percent error of the fit for dataset 5, where m ¯ S = 96 p e .
Fig. 7.
Fig. 7. Azimuthal average of S / N R for the six datasets.
Fig. 8.
Fig. 8. (a) Mixing efficiency η m for dataset 5, where m ¯ S = 96 p e . (b) The azimuthal average of η m for each dataset with the expected value of 32.2% in the black, dashed line.
Fig. 9.
Fig. 9. (a) Calculated frame of the signal noise efficiency η S for dataset 5 where m ¯ S = 96 p e . (b) The azimuthal average of η S for each dataset.
Fig. 10.
Fig. 10. Power regression (dashed line) of m ¯ S versus E ¯ S showing the signal noise energy E ¯ S was proportional to the square of the per-pixel mean number of signal photoelectrons m ¯ S and not linear like shot noise.
Fig. 11.
Fig. 11. (a) Measured SNR S / N for dataset 5, where m ¯ S = 96 p e . (b) The azimuthal average of S / N for each dataset.
Fig. 12.
Fig. 12. (a) Total system efficiency η T for dataset 5 where m ¯ S = 96 p e . (b) The azimuthal average of η T for each dataset.
Fig. 13.
Fig. 13. Pixel averaged measured total system efficiency η T for the six datasets, where the width of the error bars represent the standard deviation, the dashed line represents the expected value of 22.7%, and the dotted lines are ± σ η T = 6.5 % .
Fig. 14.
Fig. 14. (a) Mean number of reference photoelectrons m ¯ R ( x , y ) and (b) mean reference noise energy E ¯ R ( x , y ) for the previously conducted experiment.

Tables (6)

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Table 1. Expected System Efficiencies

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Table 2. Pixel- and Frame-Averaged Values with Respect to the Six Datasets

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Table 3. Gaussian Fit Results with Respect to the Six Datasets

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Table 4. Mixing and Reference-Noise Efficiency Measurements

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Table 5. Updated System Efficiencies

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Table 6. Previous Experiment Details

Equations (19)

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i H ( x , y ) = | U S ( x , y ) + U R ( x , y ) | 2 ,
U ^ S ( x , y ) = g A / D τ p 2 h ν U R * U S ( x , y ) + g A / D π 4 q I 2 σ n ( x , y ) 2 N k ( x , y ) ,
q I = λ z I p d p ,
σ n 2 ( x , y ) = m ¯ R + m ¯ S ( x , y ) + σ r 2 ,
S / N ( x , y ) = η T E { | U ^ S ( x , y ) | 2 } V { U ^ S ( x , y ) } ,
E { | U ^ S ( x , y ) | 2 } = g A / D 2 m ¯ S ( x , y ) m ¯ R ,
V { U ^ S ( x , y ) } = g A / D 2 π 4 q I 2 σ n 2 ( x , y ) .
S / N ( x , y ) = η T 4 q I 2 π m ¯ S ( x , y ) m ¯ R m ¯ R + m ¯ S ( x , y ) + σ r 2 .
S / N ( x , y ) η T 4 q I 2 π m ¯ S ( x , y ) .
S / N R ( x , y ) = ρ π λ 2 τ h ν P o ( M T x o , M T y o ) A o ,
η T ( x , y ) = η t η q η m η R η S ( x , y ) .
η s = w ( f x , f y ) sinc 2 ( p f x , p f y ) ,
G ( x , y ) = A exp ( 1 2 ( x x c σ x ) 2 + ( y y c σ y ) 2 ) ,
r G ( x , y ) = ( x x c 2 ln ( 2 ) σ x ) 2 + ( y y c 2 ln ( 2 ) σ y ) 2 ,
η m ( x , y ) = E ¯ H ( x , y ) E ¯ N ( x , y ) m ¯ R ( x , y ) m ¯ S ( x , y ) .
η R = π 4 q I m ¯ R E ¯ R ,
η S ( x , y ) = E ¯ R ( x , y ) E ¯ N ( x , y ) .
S / N ( x , y ) = E ¯ H ( x , y ) E ¯ N ( x , y ) E ¯ N ( x , y ) ,
η T ( x , y ) = 1 η S ( x , y ) S / N ( x , y ) S / N R ( x , y ) .

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