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I am a retired Physicist (born in 1941) with experience in chemistry, Fourier optics, image intensifiers, quantum logic, quantum physics, modular software. Stumbled into the quaternion waltz (c=ab/a)... Read More »

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Aug 19 2010 | comment(s)

A long time ago (≈1975) I was involved in establishing a world standard for the measurement of the Optical Transfer Function (OTF). It is better known as its modulus, the Modulation Transfer Function (MTF). The OTF combines the MTF with the Phase Transfer Function (PTF). The OTF is a two dimensional Fourier transform of the Point Spread Function (PTF). Thus, it is a two dimensional frequency characteristic used for qualifying imaging devices and chains of imaging devices.

Since the image of a point contains very little energy, the OTF is measured by analyzing the Line Spread Function (LSF).

The redefiner Ɽt can be mimicked by a trail of infinitesimal unitary transforms. Each subsequent trail element has eigenvectors that differ from those of its predecessor. These eigenvectors are also eigenvectors of Ɽt. For a single vector, which is not an eigenvector of Ɽt, the action of Ɽt can be represented by the integrated activity of this trail on that vector. This can be interpreted as the activity of a genuine unitary transform Ut. When a redefiner Ɽt is applied to the eigenvector |q> of an operator Q with eigenvalue q, then the eigenvector is transferred into another vector |Ut q>. The expectation value for |QUt q> is no longer q, but
Optics normally treats the behaviour of packages of light waves (photons). However, when passing through appropriately shaped fields, particles may behave similar as photons. A beam of electrons that is not too dense will under such conditions behave similar to light beams that pass comparable lenses. In a dense beam the electrons will influence each others path via their own Coulomb field.

The OTF

Dynamic quantum logic

Abstract

I thought that I knew what a unitary transform is, until I started thinking about it.
(2^n-ons are hypercomplex numbers that are related via the 2^n-on construction. Including n=3 the 2^n-on construction gives the same numbers as the Cayley-Dickson construction. From there the 2^n-ons are "nicer".)

I know the following: