Two-dimensional weak-object transfer functions in the scanning harmonic microscope

Abstract

The two-dimensional imaging properties of scanning harmonic microscopes are considered. The two-dimensional weak-object transfer functions for non-confocal (point source and large-area incoherent detector) and confocal (point source and point detector) scanning harmonic microscopes are calculated. Results show that the harmonic microscopes are capable of super-resolution in that the spatial frequency cut-off is twice that for a microscope working at the fundamental wavelength. Confocal scanning harmonic microscopes exhibit better resolution than the conventional type.     

Vectorial, high-numerical-aperture study of phase-contrast microscopes

We describe, using a high-numerical-aperture vectorial model, the image formation of phase-contrast microscopes. In particular, imaging of a weak phase object is considered. We show that, partly owing to the fact that phase-contrast microscopes are interference microscopes, their image formation is fundamentally different from that of conventional transmission optical microscopes. Our detailed analysis reveals a number of yet undocumented properties of these microscopes, including that depending on the given configuration, they can exhibit an improved lateral resolution when larger detectors are used in comparison with that obtained for a small detector size. We present numerical examples to explain this phenomenon and discuss our analysis in detail.     

Image Formation in the Scanning Microscope

Fourier imaging in the scanning microscope is considered. It is shown that there are two geometries of the microscope, which have been designated Type 1 and Type 2. Those of Type 1 exhibit identical imaging to the conventional microscope, whereas those of Type 2 (confocal microscopes) display various differences. Imaging of a single point object, two-point resolution and response to a straight edge are also considered. The effect of various arrangements using lenses with annular pupil functions is also discussed. It is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with annular pupils.     

Theory for double beam interference microscopes with coherence effects and verification using the linnik microscope

Abstract

A theoretical model for the interferogram from double beam interference microscopes, which takes into account the coherence effects, is presented. The model is based on the general imaging theory of a lens in defocus. For the case of zero relative lateral displacements between the reference and object beams a simplified expression is found for the defocus and path length dependence of the interferogram. Based on this expression the characteristics of the interferogram are studied and special attention is devoted to explaining the dependence of the fringe size on the objective numerical aperture, and the effect of the spatial and temporal coherence. For the Linnik microscope in which two objectives and a beam splitter cube are used, the effect of the mismatch between chromatic aberrations of the two objectives, and the effect of glass dispersions and misalignment of the beam splitter cube are investigated. Experimental results using the Linnik microscope are presented and they confirm the proposed model.     

Theory for confocal and conventional microscopes imaging small dielectric scatterers

Abstract

In this paper we develop the theory of confocal microscopes imaging small scatterers. Since scattering is a polarization dependent phenomenon we employ a full vectorial theory to treat this problem. This approach permits us to consider both imaging in high aperture systems as well as image formation in polarized light microscopy. We extend previous theories by including effects of the finite sized detector apertures. Numerical examples are presented for the most important cases. The results of the full vectorial theory are compared with those obtained from low aperture paraxial theory.     

Ray-tracing and Aberration Formulae for a General Optical System

Abstract

All aspects of the ray-tracing and of the calculation of the monochromatic and chromatic aberrations for a completely general optical system are treated. These include the specification of the system, the ray-tracing formulae for refraction, reflection and transfer, the introduction of pseudo-paraxial variables in the object and image spaces, the determination of the pupil domain and the best image plane, plus calculation of aberrations along rays. Hopkins' canonical coordinates are employed in the object and image space to facilitate the calculation of the aberration polynomial coefficients, for use in the evaluation of diffraction-based image criteria, such as the point spread function. All the formulae involved are always determinate and of good accuracy, no matter whether the object, image or either pupil, of the system is at finite distance or at infinity.     

Two-point optical resolution with homogeneous,evanescent and self field: Resolution criterion in near field imaging

Abstract

The radiative and non-radiative electromagnetic field of a quantum particle is studied. An optical resolution criterion is proposed in terms of the two-point resolution. Resolution of optical microscopes is limited either by homogeneous diffraction (conventional microscopes) or by evanescent diffraction (near-field microscopes). The evanescent diffraction limit is a function of the wavelength and the observation distance (a portion of the wavelength), which may be circumvented by measuring the non-radiative field, namely the self field in the quantum range of the objects. The resolution then becomes a function of the object size, and is no longer limited by the wavelength of light used. The two-level hydrogen atom is taken as an example.     

Rainbow holography of a diffuse three-dimensional object with a synthetic slit

Abstract

A study of rainbow holography with a movable synthetic slit in three-dimensional (3D) space is presented. A diffuse 3D object and an imaging lens are translated uniformly along the same direction with different (or identical) speeds in the X-Y plane. The spatial frequencies of the coherent wave illuminating the object are α, 0 and γ. As a result, the synthetic slit in rainbow holography is presented at a position which depends on the translational direction of the object and the imaging lens, their relative speeds, the spatial frequency of the illuminating wave in the X ₀ direction, and the relative distance of the reference source and the reconstruction source from the holographic plate. Theoretical analysis and some experimental results are presented.     

An illumination and highlights invariant colour model for image matching

Abstract

Colour can provide critical information for a variety of computer vision tasks such as image matching, object recognition and image retrieval. However, for it to be useful in practice, the colour model used to represent the intrinsic properties of the imaged objects must be insensitive of imaging conditions such as lighting geometry, illumination colour and highlights. In this paper, we present a colour model for image matching and object recognition that is invariant for illumination and highlights. The colour model is defined as the ratios of the colour differences between neighbouring pixels for each colour component. Based on the dichromatic reflection colour model, it is shown that the proposed colour model is invariant to lighting geometry, illumination colour, highlights and diffuse lighting. Experimental results show robust image matching using the proposed colour model on objects that are illuminated under different illumination colours and lighting geometry. The proposed colour model can be used as a prepossessing step for applications where limited or no constraints on the imaging process can be imposed.     

Structural Information of the Volume Hologram from Mie Scattering

Abstract

Using Mie scattering theory, the imaging process of the volume hologram is described. The eigenequation and its integral kernel are obtained. Expressions for the maximum information density and for structural information are derived. Computations of eigenfunctions and eigenvalues for a two-dimensional object are presented.     

Partially Coherent Imaging of a Straight-edged Object Associated with Periodic Structures of Acoustically Modified Spatial Coherence

Abstract

Spatial coherence of laser light can be modified by a progressive ultrasonic wave. The resultant optical mutual intensity has lateral and longitudinal periodicities in the near field behind the ultrasonic cell. Over the near field the longitudinal periodicity is lost in any plane parallel to the output plane of the cell but the lateral periodicity still remains. Such a plane serves as an object plane for partially coherent imaging. The imaging characteristics of an edge object, depending on various ultrasonic parameters, are described. Ringing suppression and contrast enhancement occur satisfactorily in the image if the ultrasonic parameters are properly controlled. Theoretical predictions are in good agreement with the experimental results.     

Quantum Statistical Properties of Coupled Nonlinear Oscillators with Losses

Abstract

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.     

Double Passage Imaging Through a Random Screen Using a Non-redundant Aperture

Abstract

When a deterministic object situated in the near or far-field is coherently illuminated and viewed through the same random screen, the time-averaged image contains diffraction-limited information. We demonstrate that the use of a non-redundant aperture considerably simplifies the retrieval of this information. The effects of the number of sub-apertures, finite sub-aperture size and finite exposure time on the imaging process are discussed. The optimal procedure for recovery of object spatial frequencies is shown to be sequential, using a two pinhole or Michelson-Fizeau aperture. Computer-simulated reconstructions of simple object distributions are presented.     

Analytical and Numerical Approximations in Fresnel Diffraction

Abstract

Procedures for the fast and accurate numerical computation of Fresnel diffraction integrals are developed on the basis of geometrical properties of the Cornu spiral. The methods proposed allow the highly oscillatory integrals in Fresnel diffraction to be approximated by means of three simpler integrals and permit the calculation of these final integrals using analytical formulae.     

Meetings Calendar

Abstract

Reduced (fractional) coordinates (σ, τ; x y) are defined for the object and image planes and for the paraxial entrance and exit pupils. These coordinates are defined to give exact values of the direction cosines and the coordinates of suitable points on the corresponding rays in the initial object space. For a ray in any other space of the optical system, its direction cosines and the coordinates of its point of incidence at a surface are represented by power series in (σ, τ; x y), and the corresponding paraxial quantities are defined to be the coefficients of the linear terms. The customary paraxial refraction and transfer equations for rays then appear as exact algebraic relations between these coefficients. The customary ambiguity in the significance of the paraxial approximations and formulae is thereby removed, and paraxial theory is put on the rigorous basis necessary for its applications, using methods that are immediately applicable to (for example) systems containing media of non-uniform refractive index.     

Discharge estimation in compound channels with fixed and mobile bed

Two-dimensional (2-D) formulae for estimating discharge capacity of straight compound channels are reviewed and applied to overbank flows in straight fixed and mobile bed compound channels. The predictive capabilities of these formulae were evaluated using experimental data obtained from the small-scale University of Birmingham channel. Full details of these data and key references may be found at the following www.flowdata.bham.ac.uk (university website). 2-D formulae generally account for bed shear, lateral shear, and secondary flow effects via 3 coefficients f, λ and Γ In this paper, the secondary flow term (Γ) used within the 2-D methods analysed here is ignored in all applications. Two different 2-D formulae almost give practically the same results for the same data when the secondary flow term is ignored. For overall test cases, the value of dimensionless eddy viscosity λ used in 2-D formulae was kept at 0·13 as recommended for open channels. 2-D formulae gave good predictions for most of the data sets studied in comparison with the traditional 1-D methods, namely the Single Channel Method (SCM) and the Divided Channel Method (DCM). The accuracy of predictions of 2-D formulae was increased by calibrating of λ value where the calibration was needed. For overall data, the average errors for each method were Lateral Division Methods (LDMs), with λ value of 0·13, 2·8%, DCM 14·3% and SCM −26·8%. The average error was 0·5% for LDMs with the calibrated values of λ     

Image Intensity at the Edge of a Straight Edge Object

Abstract

We consider the value of the intensity image at the geometrical position of a general, flat, straight edge object. We adopt a Fourier optical transfer function approach and obtain, rigorously, analytic expressions for the cases of coherent, incoherent and equal aperture, partially coherent imaging. Aberration-free, circular pupils are considered and the analytic results are found to agree with earlier numerical calculations. We also obtain expressions for the intensity gradient at the edge.     

Coherent Imaging Through a Random Screen

Abstract

Recent work on imaging coherently illuminated objects through a time-varying random screen has demonstrated the possibility of recovering the Fourier modulus of the object spectrum. We suggest an approach which, although limited to restricted conditions, enables both the modulus and the phase of the object to be recovered from the time-averaged image spectrum.     

The Generalised Lau Effect

Abstract

It has been shown that the process of coded imaging of incoherently illuminated extended objects by self-imaging structures (SIS) naturally leads to the formation of Lau-type fringes at finite conjugates. The object grating and the grating representing the SIS need not be of the same period. The generalised Lau fringes are obtained under a conjugate relation characteristic of the SIS imaging and a general matching condition involving the periods and frequencies of the two periodic structures. The classical Lau fringes and the so-called finite conjugate classical Lau fringes are formed under special imaging conditions. Useful applications have been mentioned.     

New Approximation for Partially Coherent Imaging of Straight Edges

Abstract

Partially coherent imaging occurs especially in microscopy and microlithography. The imaging properties of such systems are described by the ‘bilinear transfer function’ (BTF). This paper deals with an approximation of the BTF for conventional microscopy. The approximation allows the analytical calculation of image intensity distributions and the use of a combination of two transfer functions for the amplitude transmission spectrum. Examples of calculations of intensity distributions in the imaging of straight edges are given and compared with exact calculations.