J. H. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547-1569 (2009).

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56, 2029-2033 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[CrossRef]
[PubMed]

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Networking 4, 501-516 (2005).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938-1941 (1999).

[CrossRef]

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52, 4930-4940 (1995).

[CrossRef]
[PubMed]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations,” Ann. Math. Stat. 23, 493-507 (1952).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

C. M. Caves, “Quantum mechanical noise in an interferometer,” Phys. Rev. D 23, 1693-1708 (1981).

[CrossRef]

H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations,” Ann. Math. Stat. 23, 493-507 (1952).

[CrossRef]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938-1941 (1999).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Networking 4, 501-516 (2005).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[CrossRef]
[PubMed]

P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” presented at the 14th Coherent Laser Radar Conference, Snowmass, Colorado, 9-13 July 2007.

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Networking 4, 501-516 (2005).

[CrossRef]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52, 4930-4940 (1995).

[CrossRef]
[PubMed]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56, 2029-2033 (2009).

[CrossRef]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938-1941 (1999).

[CrossRef]

P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” presented at the 14th Coherent Laser Radar Conference, Snowmass, Colorado, 9-13 July 2007.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[CrossRef]
[PubMed]

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52, 4930-4940 (1995).

[CrossRef]
[PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[CrossRef]
[PubMed]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).

J. H. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547-1569 (2009).

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Networking 4, 501-516 (2005).

[CrossRef]

J. H. Shapiro, B. A. Capron, and R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292-3313 (1981).

[CrossRef]
[PubMed]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56, 2029-2033 (2009).

[CrossRef]

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, 1968).

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56, 2029-2033 (2009).

[CrossRef]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938-1941 (1999).

[CrossRef]

P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” presented at the 14th Coherent Laser Radar Conference, Snowmass, Colorado, 9-13 July 2007.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations,” Ann. Math. Stat. 23, 493-507 (1952).

[CrossRef]

J. H. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547-1569 (2009).

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56, 2029-2033 (2009).

[CrossRef]

J. H. Shapiro, S. Guha, and B. I. Erkmen, “Ultimate channel capacity of free-space optical communications,” J. Opt. Networking 4, 501-516 (2005).

[CrossRef]

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52, 4930-4940 (1995).

[CrossRef]
[PubMed]

D. J. Wineland, J. J. Bollinger, W. M. Itano, and F. L. Moore, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A 46, R6797-R6800 (1994).

[CrossRef]

C. M. Caves, “Quantum mechanical noise in an interferometer,” Phys. Rev. D 23, 1693-1708 (1981).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[CrossRef]
[PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).

[CrossRef]
[PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938-1941 (1999).

[CrossRef]

P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” presented at the 14th Coherent Laser Radar Conference, Snowmass, Colorado, 9-13 July 2007.

B.Bhanu, D.E.Dudgeon, E.G.Zelnio, A.Rosenfeld, D.Casasent, and I.S.Reed, eds., Special Issue on Automatic Target Recognition, IEEE Trans. Image Process.6 (1997).

G.W.Kamerman, ed., Selected Papers on LADAR, SPIE Milestone Series, Vol. MS133 (SPIE, 1997).

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).

Strictly speaking, the soft aperture must be embedded inside a hard-aperture pupil, e.g., A(ρ′)=e−2|ρ′|2/R2 for |ρ′|≤D/2 and A(ρ′)=0 otherwise. Without appreciable loss of generality we shall ignore that constraint here and in Section because: (1) we are interested in soft apertures whose transmission at the hard-aperture limit is <1%; and (2) we will not be assuming so much SVI and PSA that the hard-aperture limit will constrain the soft-aperture resolution improvement afforded by these quantum enhancements. We shall, however, impose the hard-aperture limit in Section , when we employ MTF analysis to generate simulated baseline and quantum-enhanced imagery.

One-to-one imaging corresponds to setting F=L in Fig. , a choice that simplifies the notation. In reality, of course, the target range will satisfy L≫F, however, this merely introduces a minification factor into the analysis.

This equal-strength assumption makes the LADAR's task of distinguishing between the one-target and two-target hypotheses entirely a matter of the spatial pattern in the image plane rather than detected target-return strength.

Strictly speaking, |T(x″)|≤1 is required. However, because of the quasi-Lambertian nature of the target reflection, the simple expressions we have provided lead to appropriate statistics for the classical target-return field arriving at the LADAR receiver's entrance pupil.

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Wiley, 1968).

Strictly speaking π/2 is the maximum value of θ0. It is only because we are employing paraxial optics that θ0—>∞ appears to be possible. In practice, however, we will never be concerned with angular separations that take us outside the realm of paraxial optics.

Our Gaussian soft-aperture definition for Rayleigh resolution is chosen so that the depth of the trough between the average photon-flux density of the two point targets on the detector array is equal to the trough depth present for the same two targets when they are imaged through an unobscured hard pupil of length D and they are separated by the hard-aperture Rayleigh angle 2θ0=λ/D.

Alternatively, for stationary targets, we can use a two-pulse illumination sequence, with the first pulse employed to image the real quadrature and the second pulse employed to image the imaginary quadrature, to achieve similar results.

Once again we are violating |T|≤1, and once again our field-reflection model does not pose a problem in that it gives physically reasonable statistics for the Fraunhofer-diffracted target return that is collected by the LADAR's entrance pupil.