Geometric theory of the grating is developed, with special emphasis on the relation between the properties of holographic gratings and those of mechanically ruled gratings. The theory is applicable to practically all types of holographic and mechanically ruled gratings, including aspheric gratings. General expressions are given for the effective grating constant, the grating equation, the focal curves, and the light-path function. Possible applications of the theory to the design of aberration-corrected gratings are also described.

Geometric theory of the grating

Since its discovery during the 1930s the Cerenkov effect (light emission from charged particles traveling faster than the local speed of light in a dielectric medium) has been paramount in the development of high-energy physics research. The ability of the emitted light to describe a charged particle’s trajectory, energy, velocity, and mass has allowed scientists to study subatomic particles, detect neutrinos, and explore the properties of interstellar matter. However, to our knowledge, all applications of the process to date have focused on the identification of particles themselves, rather than their effect upon the surroundings through which they travel. Here we explore a novel application of the Cerenkov effect for the recovery of the spatial distribution of ionizing radiation energy deposition in a medium and apply it to the issue of dose determination in medical physics. By capturing multiple projection images of the Cerenkov light induced by a medical linear accelerator x-ray photon beam, we demonstrate the successful three-dimensional tomographic reconstruction of the imparted dose distribution.

Three-dimensional Čerenkov tomography of energy deposition from ionizing radiation beams

Several conventional methods for absolute sphericity testing of optical surfaces are known. One method has been used previously for real time interferometry, but a detailed investigation has not been carried out so far. In this work the known conventional methods are reviewed and assessed for suitability in real time interferometry. One method has been applied to phase stepping interferometry and examined. Adjustment peculiarities, experimental results of deviation measurements on normal surfaces, and application of normals are reported. Measuring errors, especially coherent noise, are analyzed and a special subsequent digital spatial filtering technique for diminution of noise is described.

Absolute sphericity measurement

A method of tracing rays through holographic gratings, both plane and concave, is developed The method is applicable not only to holographic gratings, but also to mechanically ruled gratings with variable spacing and curved grooves Some examples are given in the form of spot diagrams for certain specific cases A modification of the method is also described to apply to aspheric gratings

Ray tracing through holographic gratings

Publisher Summary This chapter discusses the aberration theory of gratings and grating mountings and reviews the properties of spectroscopic grating systems from the point of view of aberration theory The chapter focuses on the properties of concave grating mountings and aberrations of plane grating mountings, which arise from the focussing optics Monochromators are systems with an entrance slit and exit slit They are essentially for photo-electric use, and spectrographs, in which a considerable range of spectrum is imaged on to some kind of image storage system The chapter also focuses on the effects of the differentiation on the optical design of the spectroscopic system

VI Aberration Theory of Gratings and Grating Mountings

A total aberration formula is defined as one which gives total ray or optical path aberration from finite raytrace data. Some known expressions of this kind are reviewed and a new expression for optical path aberration along skew rays is developed; this expression gives the maximum possible conservation of numerical precision.

A New Total Aberration Formula

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.

Some Experiments on Precision Lens Centring and Mounting

A method for tracing exact skew rays through spherical concave reflecting gratings is developed; modifications for plane gratings and for gratings ruled on toric and ellipsoidal blanks are indicated

Tracing Skew Rays through Concave Diffraction Gratings

Tolerances of Strehl intensity type are derived for imagery of a line by a rectangular pupil, as in spectroscopic instruments.

Aberration Tolerances for Spectrum Line Images

Synthetic aperture radar operated from a satellite in Earth orbit poses some new problems in the design of an optical system to reconstruct the radar picture. We state these problems and indicate suitable solutions for a coherent optical processor.

W.T. Welford

Papers

A New Total Aberration Formula

Some Experiments on Precision Lens Centring and Mounting

Tracing Skew Rays through Concave Diffraction Gratings

Aberration Tolerances for Spectrum Line Images

Optical Decoding of Satellite-borne Synthetic Aperture Radar