Showing papers in "Journal of Modern Optics in 1974"
TL;DR: In this article, the time dependence of ρ11, ρ22 and ρ12 under steady-state conditions was analyzed under a light field interaction V = -μ12Ee iωt + c.c.
Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>
1,872 citations
TL;DR: A computational procedure is devised which must reduce a defined ‘error energy’ which is implicit in the truncated spectrum and it is demonstrated that by so doing, resolution well beyond the diffraction limit is attained.
Abstract: A new view of the problem of continuing a given segment of the spectrum of a finite object is presented. Based on this, the problem is restated in terms of reducing a defined ‘error energy’ which is implicit in the truncated spectrum. A computational procedure, which is readily implemented on general purpose computers, is devised which must reduce this error. It is demonstrated that by so doing, resolution well beyond the diffraction limit is attained. The procedure is shown to be very effective against noisy data.
1,056 citations
TL;DR: In this paper, modulation transfer functions of the dioptrics of the human eye for white (equal energy distribution) light were calculated for different pupil sizes from experimental data on the aberrations.
Abstract: Modulation transfer functions of the dioptrics of the human eye for white (equal energy distribution) light were calculated for different pupil sizes from experimental data on the aberrations. The largest aberration is the chromatic difference of focus. Since this aberration is well known quantitatively and is subject to small individual differences only, the calculated modulation transfer functions can be considered as representative for human eyes in general. The present calculations, the fundus reflection measurements of the line-spread function by Campbell and Gubisch [1], and the measurements of retinal scattering by Ohzu and Enoch [2] confirm each other. Modulation transfer functions were also calculated for just noticeable focusing errors, and may be informative on the tolerance limit to visual image quality. The calculations have been extended to the special conditions of vision at low luminances.
223 citations
TL;DR: Theoretical counterparts for the experimental efficiency curves obtained by Hutley and Bird in the visible region for a holographic grating covered consecutively with films of silver, aluminium and gold are presented in this paper.
Abstract: Theoretical counterparts are presented for the experimental efficiency curves obtained by Hutley and Bird in the visible region for a holographic grating covered consecutively with films of silver, aluminium and gold. It is thus shown that the recently developed formulation of Maystre, which takes into account the finite conductivity of the grating surface, gives results in quantitative agreement with experiment. This not only validates the theory, but also demonstrates that the difficulties associated with profile determination and oxide films, which have in the past led some experimenters to renounce the visible region and perform measurements on millimetre-wave gratings, are not in fact insuperable. It is also shown that only a theoretical model which takes into account groove depth effects can hope to predict accurately the locations of regions of enhanced energy absorption by gratings.
63 citations
TL;DR: In this article, the first order probability density function of the intensity in a speckle pattern is considered as a function of spectral bandwidth of the incident light, and it is shown that the sta...
Abstract: Moments and the first order probability density function of the intensity in a speckle pattern are considered as a function of the spectral bandwidth of the incident light. It is shown that the sta...
55 citations
TL;DR: The transfer function of the human lens system appears to be strongly influenced by the possibility to predict the input signal, and the two aforementioned transfer functions are compared with sinusoidal responses which were strongly influencedby the extent of training and the attention of the subject.
Abstract: The transfer function of the human lens system appears to be strongly influenced by the possibility to predict the input signal. Owing to this the accommodating system can respond very rapidly to a change in target distance when anticipation is used, and it is relatively slow when the subject is unable to anticipate the input signal. An optimal and a minimal transfer function is determined assuming that possibility to anticipate the input signal is relevant. The two aforementioned transfer functions are compared with sinusoidal responses which were strongly influenced by the extent of training and the attention of the subject.
52 citations
TL;DR: In this paper, a technique for cross-correlating a one-dimensional input signal with a library of stored reference signals simultaneously is discussed, which involves the linear scanning of a temporally modulated image of a photographic reference mask across a temporal-integrating read-out device.
Abstract: This paper will discuss a technique for cross-correlating a one-dimensional input signal with a library of stored reference signals simultaneously The technique involves the linear scanning of a temporally-modulated image of a photographic reference mask across a temporally-integrating read-out device First, a physical feeling for the technique is given, followed by a mathematical analysis, a description of a breadboard system now in operation, a simple experiment to demonstrate the correlators features, and a mention of some alternate configurations desirable for specific applications
30 citations
26 citations
TL;DR: In this paper, les franges presentent des proprietes interessantes, en particulier celle de n'etre visibles qu'en certains endroits seulement, c'est-a-dire d'etres localisees.
Abstract: La reconstitution simultanee par holographie des images d'un objet avant et pendant une sollicitation mecanique fait apparaitre des franges d'interference. Ces franges presentent des proprietes interessantes, en particulier celle de n'etre visibles qu'en certains endroits seulement, c'est-a-dire d'etre localisees. Ces phenomenes ont deja ete examines en detail par plusieurs auteurs auxquels sont empruntes certains raisonnements. Pour chaque point de la surface du corps, on peut observer les franges avec un systeme optique visant dans une direction variable. Sur une courbe de l'espace est remplie la condition de localisation complete: les ondes se superposant en ces points ont meme difference de phase. Pour chaque direction, on peut aussi donner l'endroit ou le contraste des franges est maximum: on se trouve ainsi sur une surface de localisation partielle. Grâce a un critere sur l'orientation des franges, il est possible de determiner les points de localisation complete et d'en deduire par une relation lin...
26 citations
TL;DR: In this paper, it is established that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object.
Abstract: It is re-established, in a suitable form, that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object. This result is employed to determine the path difference equations for the wavefront forming the interference pattern as observed in three orthogonal directions. A set of linear equations is derived which is shown to relate the components of a small general surface displacement to the fringe spacing and localization plane of the observed interference pattern. The practical application of the theory is then discussed. Numerical equations are derived for various geometries of interferometer and in particular the measurements of rigid-body translations and plane strain are dealt with. In addition it is shown how problems that arise in the measurement of complicated surface displacements may be considerably simplified.
23 citations
TL;DR: In this paper, an approximate theory of the effects of these two types of error on turning value monitoring is developed and the results are used to devise a modification to the conventional technique which enables filter performance much nearer theoretical to be achieved.
Abstract: Errors which occur during the deposition of thin film narrow-band optical filters can be classified as either static or dynamic. An approximate theory of the effects of these two types of error on turning value monitoring is developed and the results are used to devise a modification to the conventional technique which enables filter performance much nearer theoretical to be achieved.
TL;DR: In this article, the formation and contrast of Fourier images of a periodic object, especially a sinusoidally transparent object, are investigated under partially coherent illumination, and it becomes apparent that the spatial coherence of light affects seriously the contrast and positions of the Fourier image planes.
Abstract: The formation and the contrast of Fourier images of a periodic object, especially a sinusoidally transparent object, are investigated under partially coherent illumination. It becomes apparent that the spatial coherence of light affects seriously the contrast of Fourier images and the positions of the Fourier image planes.
TL;DR: In this paper, the lens cells were assembled in plain diamond turned barrels and the symmetry was improved by an order of magnitude over results previously reported, and the results were shown to be consistent with the results reported in this paper.
Abstract: Centring was done by interferometric measurement of surface height and the lens cells were assembled in plain diamond turned barrels; improvements in symmetry of about an order of magnitude over results previously reported were found.
TL;DR: In this paper, a theoretical analysis of single and dual beam scattering flowmeters is given, taking their Gaussian characteristics into account, and the average power spectrum of the detector signal is derived as a function of the particle concentration.
Abstract: A theoretical analysis is given of single and dual beam scattering flowmeters. All propagating beams are treated rigorously, taking their Gaussian characteristics into account. An exact derivation of the Doppler frequency shows how it depends on the position of the scattering particle within the scattering volume. The spatial and spectral resolutions of both Doppler systems are given. It is shown in what way these depend on the geometry of the optical arrangement. The average power spectrum of the detector signal is derived as a function of the particle concentration. The signal-to-noise ratios of both systems are calculated and compared. Some inherent differences between the two systems will be pointed out.
TL;DR: In this paper, an expression for the average power spectrum of the speckle in the image of a coherently illuminated diffusing object was derived when a number of exposures are superimposed with a shift of the sampling aperture located in the spatial frequency plane between successive exposures.
Abstract: One method which has been suggested for reducing speckle in the holographically reconstructed image of a diffusing object is the use of a moving aperture in the pupil plane of the imaging lens (this is equivalent to sampling the spatial frequency spectrum of the object). An expression is derived for the average power spectrum of the speckle in the image of a coherently illuminated diffusing object when a number of exposures are superimposed with a shift of the sampling aperture located in the spatial frequency plane between successive exposures, and experimental results are presented which confirm that an appreciable reduction in speckle can be obtained even when the shift of the sampling aperture between two exposures is less than its dimensions. This analysis is then extended to the case of a rectangular sampling aperture which is moving continuously for the duration of the exposure. The results show that, for a given range of movement, an exposure with a continuously moving aperture should be more effe...
TL;DR: In this article, a computer program has been developed and calculated results are compared with measurements, and the formulae necessary to extend from the monochromatic to the polychromatic OTF are developed for the axial case.
Abstract: Polychromatic or white-light OTF is put forward as a criterion of image quality for systems under actual working conditions. The formulae necessary to extend from the monochromatic to the polychromatic OTF are developed for the axial case. A computer programme has been developed and calculated results are compared with measurements.
TL;DR: In this article, it was shown that the usual paraxial theory for the Hermite Gaussian or Laguerre Gaussian beams, produced by some lasers, can be replaced by a more general theory which is precise according to Maxwell's equations.
Abstract: An electromagnetic beam is defined using mathematical properties of the associated angular spectrum of plane waves. It is found that the usual paraxial theory for the Hermite Gaussian or Laguerre Gaussian beams, produced by some lasers, can be replaced by a more general theory which is precise according to Maxwell's equations. In this theory the beams exhibit an amplitude distribution over any plane normal to the direction of propagation which can be described using prolate spheroidal wave functions. As the degree of collimation is increased, these beams asymptotically take on the familiar Gaussian amplitude cross section. However, as the divergence from focus is increased, these beams asymptotically approach modified dipole fields. It is found that two, mutually exclusive, classes of beam fields exist. For each beam in one class there is always a complementary beam in the other class. As the degree of collimation is increased, complementary beams become almost identical. Complementary beams contain elect...
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TL;DR: It is shown that when a perpendicularly stretched thread is fixated at its centre with the eyes in symmetrical convergence, the thread has to be tilted around the fixated point with its top away from the observer towards the observer.
Abstract: When a perpendicularly stretched thread is fixated at its centre with the eyes in symmetrical convergence, the thread has to be tilted around the fixated point with its top away from the observer for it to appear perpendicular. This fact was recognized by a number of investigators as early as the 1850's. For this reason both Hering and Helmholtz described the horopter as an ‘upside-down’ cone. The present investigation employs a twin point-light source apparatus to estimate the orientation and the shape of a subjective equidistant line that lies in the median plane of the observer. Since the method of measurement depends on retinal disparity clues, this locus corresponds to the stereoscopic frame of reference in the median plane. The results are in qualitative agreement with previous findings. Quantitatively, however, they show a much smaller tilt of the reference plane than the ones reported by Helmholtz and others. The stereoscopic sensitivities of the retinal regions at the various elevations above and...
TL;DR: For the case of holographic interferometry when one measures changes in position and shape of diffusely reflecting surfaces new, quite general relations determining the localization of interference fringes are derived as mentioned in this paper.
Abstract: For the case of holographic interferometry when one measures changes in position and shape of diffusely reflecting surfaces new, quite general relations determining the localization of interference fringes are derived. The important properties of fringe localization are also discussed and a useful practical solution is drawn.
TL;DR: In this paper, the spectral properties of multilayer dielectric thin films are investigated for different states of polarizations p and s even when the incoming light is unpolarized, and the difference between both spectra of the two states of polarization is regarded as the polarization effect.
Abstract: The spectral behaviour of the reflected and transmitted light from a dielectric multilayer film at an oblique angle of incidence is discussed. These spectra are different for both states of polarizations p and s even when the incoming light is unpolarized. The difference between both spectra of the two states of polarization is regarded as the polarization effect. This effect is investigated for three cases: all dielectric Fabry-Perot interference filters (ADI), Long and Short-wave Pass Filters (LWPF and SWPF) and multilayer antireflection coatings (AR). The conditions for avoiding or reducing these polarization effects in multilayer dielectric thin films of the above-mentioned cases are found and applied. Typical designs and calculated spectra are given and discussed.
TL;DR: In this article, a quantitative relationship for the fluorescent intensity observed from either side of a plane parallel sheet of turbid material, has been derived based upon the simplified theory of Kubelka and Munk.
Abstract: Based upon the simplified theory of Kubelka and Munk a quantitative relationship for the fluorescent intensity, observed from either side of a plane parallel sheet of turbid material, has been derived. The fluorescing substance is assumed to be uniformly distributed throughout the bulk of the medium. The results obtained show that fluorescence measurements from either side have good linearity over a very wide range of concentrations of fluorescing substance. Measurements from either side are very nearly equivalent in this regard. As expected, the fluorescent intensity observed at the illuminated surface is higher than that observed at the exit plane. The results are intended mainly for use in the quantitative analysis of fluorescent substances dispersed in a turbid medium. Typical applications are thin-layer chromatography and electrophoresis.
TL;DR: In this article, a theoretical analysis showed that the attenuation of the power spectrum of the speckle is proportional to the square of the average transmittance of the random aperture, resulting in a loss of image contrast.
Abstract: The use of a moving, random aperture in the plane of a hologram has been recently suggested for reducing speckle in the reconstructed image of a diffusing object. A theoretical analysis shows that while the attenuation of the power spectrum of the speckle is proportional to the square of the average transmittance of the random aperture, the power spectrum of the signal is also attenuated by the same factor, resulting in a loss of image contrast. Because of this there is no overall gain. Some experimental results are presented which support these conclusions.
TL;DR: The restoration of one-dimensional linear blur is taken as an example, and methods of designing the aperture array and evaluating its performance are discussed.
Abstract: An approach to image processing is made by means of image scanning with an aperture array. The restoration of one-dimensional linear blur is taken as an example, and methods of designing the aperture array and evaluating its performance are discussed. The quality criterion of restored images with regard to resolution and detection is introduced and applied to the practical system.
TL;DR: In this article, it was shown that if a point source is placed in the neighbourhood of a plane boundary, radiation may reach a point on the same side of the boundary by a route which includes a lateral wave path in the second medium.
Abstract: It is known that if a point source is placed in the neighbourhood of a plane boundary, radiation may reach a point on the same side of the boundary by a route which includes a lateral wave path in the second medium. The flux arriving by such a lateral wave path is calculated for two cases, viz. (1) a semi-infinite, absorbing second medium and (2) a very thin absorbing film, placed between identical media.
TL;DR: Two potential causes of instability in optical flats are considered in this article, and a number of experimental results are quoted in which significant changes of figure have occurred within periods of a few years Attempts to correlate these changes with birefringence measurements have met with limited success.
Abstract: Two potential causes of instability in optical flats are considered A number of experimental results are quoted in which significant changes of figure have occurred within periods of a few years Attempts to correlate these changes with birefringence measurements have met with limited success The relative merits of glass and fused silica flats are discussed
TL;DR: In this paper, the simulation of thin-film multilayer production has been modified to take account of the influence of temperature on the performance of complete coatings in stack production.
Abstract: Computer simulation of thin-film multilayer production has shown that the effects of errors in the layers on the performance of complete coatings depends strongly on the particular monitoring process used. Deposition of dielectric quarter-wave multilayers is usually controlled by a method which involves the detection of the maxima and minima of transmission for the centre wavelength of the filter, the turning value method, and we know that this technique profits from an exceptionally efficient error compensation. The true tolerances in stack production are much larger than we would calculate neglecting this compensation. However, the analysis of experimental results shows that we must consider other effects which have so far been neglected in the computer simulation and which affect the monitoring process enough to prevent the fabrication of interference filters with very narrow transmission bands. Here we describe how the computer simulation is modified to take account of the influence of temperature cha...
TL;DR: In this article, an experimental investigation of the general equations describing holographic fringe patterns is described, and the fringe patterns resulting from known surface displacements are observed from two positions and the measured fringe spacings are compared with those predicted theoretically.
Abstract: General equations describing holographic fringe patterns have been derived in an earlier publication. In this paper an experimental investigation of the equations is described. The fringe patterns resulting from known surface displacements are observed from two positions and the measured fringe spacings are compared with those predicted theoretically. Two forms of displacement are considered: (i) rigid-body translations, (ii) linear displacement gradients. Results indicate that experimental observations are in close agreement with those predicted theoretically. The observation of plane strain is demonstrated in order to give a practical example of a problem involving a combination of the displacement classes (i) and (ii).
TL;DR: In this paper, the Stokes parameter evolution in a random medium has been studied, and the authors propose a method for the depolarization of Electromagnetic Radiation in a Random Medium.
Abstract: (1974). The Depolarization of Electromagnetic Radiation in a Random Medium: Evolution of the Stokes Parameters. Optica Acta: International Journal of Optics: Vol. 21, No. 9, pp. 721-735.