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Helstrom, C. W.

Publications and source records attributed to Helstrom, C. W..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Noncommuting observables in quantum detection and estimation theory

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a large Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Helstrom, C. W.↗
NASA NTRS1973

Optimum detection of an optical image on a photoelectric surface.

The image-detecting performance of an optimum counting detector is compared with that of a threshold detector and that of a detector basing its decisions on the total number of photoelectrons from a finite area of the image. The illuminance of the image is assumed to have a Gaussian spatial distribution. The optimum detector works with the pristine datum (and not with the photoelectric response) which is the spatiotemporal electromagnetic field at the aperture of the observing optical instrument. It is shown that little is to be gained by using details of the illuminance distribution beyond the crude knowledge of its breadth as embodied in a simple counter of emitted photoelectrons. All three detectors exhibit accordingly about the same reliability.

Helstrom, C. W.↗
NASA NTRS1973

Resolution of point sources of light as analyzed by quantum detection theory.

The resolvability of point sources of incoherent thermal light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.

Helstrom, C. W.↗
NASA NTRS1973

Application of signal detection theory to optics

Basic quantum detection and estimation theory, applications to optics, photon counting, and filtering theory are studied. Recent work on the restoration of degraded optical images received at photoelectrically emissive surfaces is also reported, the data used by the method are the numbers of electrons ejected from various parts of the surface.

Helstrom, C. W.↗
NASA NTRS1972

The application of signal detection theory to optics

The role of measurements of noncommuting quantum observables is considered in the detection of signals and estimation of signal parameters by quantum receivers. The restoration of images focused on a photosensitive surface is discussed for data as numbers of photoelectrons ejected from various parts of the surface. The detection of an image formed on a photosensitive surface in the presence of background illumination for similar data is also considered.

Helstrom, C. W.↗
NASA NTRS1972

Linear restoration of incoherently radiating objects.

Light from an incoherently radiating object and background light are focused onto a photosensitive mosaic, the currents from whose elements constitute the data on which is based a least-squares linear estimate of the radiance at points in the object. By comparison of the mean-square error with that given by Wiener filtering theory, the equivalent noise spectral density for use in the latter is shown to consist of a shot-noise term and a term due to the random fluctuations of the incoherent light; the former predominates under most circumstances. Turbulent distortion of the image after passage of the rays through a random-phase screen is also treated from this standpoint.

Helstrom, C. W.↗
NASA NTRS1972

Optimum detection of an optical image on a photoelectric surface

The detection of an optical image in the presence of uniform background light is based on a likelihood ratio formed of the numbers of photoelectrons emitted from small elements of a photoelectric surface onto which the image is focused. When diffraction is negligible and the surface has unit quantum efficiency, this detector is equipollent with the optimum detector of the image forming light. Its performance is compared with that of the threshold detector and that of a detector basing its decisions on the total number of photoelectrons from a finite area of the image. The illuminance of the image is postulated to have a Gaussian spatial distribution. All three detectors exhibit nearly the same reliability.

Helstrom, C. W.↗
NASA NTRS1972

The resolution of point sources of light as analyzed by quantum detection theory

The resolvability of point sources of incoherent light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.

Helstrom, C. W.↗
NASA NTRS1972

Noncommuting observables in quantum detection and estimation theory

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Helstrom, C. W.↗
NASA NTRS1971

Noncommunting observables in quantum detection and estimation theory

In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.

Helstrom, C. W.↗
NASA NTRS1971

The application of signal detection theory to optics

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Helstrom, C. W.↗
NASA NTRS1971

Quantum detection theory

Statistical estimation theory applied to quantum mechanics and signal detection with optical instruments

Helstrom, C. W.↗
NASA NTRS1971

Noncommuting observables in quantum detection and estimation theory

In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.

Helstrom, C. W.↗