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where the summations run from 1 to N This result is identical to the result obtained using a least-squares t of the intensity data to a sinusoidal function of the proper frequency (Eq 1466) 14143 Heterodyne Interferometry Heterodyne or AC interferometry is the general term used to describe interferometers that produce a temporal phase shift by introducing two different optical frequencies into the two arms of the interferometer Several methods exist for generating this frequency difference, the most common being moving gratings and two-frequency lasers (see Section 144) With any of these approaches, the interferogram intensity is modulated at difference in frequency (Eq (149) (1412)) The primary applications for heterodyne interferometry are distance measuring interferometry, measuring system dynamics, and surface pro lometry (Crane, 1969; Koliopoulos 1980; Sommargren, 1981; Barnes, 1987).

13 Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), and Magnetic Force Microscopy (MFM) These are variations on a method of imaging surfaces with atomic or near-atomic resolution, collectively called scanning probe microscopy (SPM) A small tip is scanned across the surface of a sample in order to construct a 3D image of the surface Fine control of the scan is accomplished using piezoelectrically induced motions If the tip and the surface are both conducting, the structure of the surface can be detected by tunneling of electrons from the tip to the surface (in STM) Any type of surface can be probed by the molecular forces exerted by the surface against the tip (in AFM) The tip can be constantly in contact with the surface, it can gently tap the surface while oscillating at high frequency, or it can be scanned just minutely above the surface.

By coating the tip with a magnetic material, the magnetic elds immediately above a surface can be imaged (in MFM) Image processing software allows easy extraction of useful surface parameters These are discussed further is Section F2 F114 Total Re ection X-Ray Fluorescence (TXRF).

Digital heterodyne interferometry (DHI) has been developed to address the need to perform high-speed analysis of dynamic systems (Massie and Nelson, 1978; Massie, 1980, 1987; Massie et al, 1979; Mottier, 1979; Massie et al 1981; Massie et al 1983; Evans, 1983) Two signi cant applications of this technology are deformable mirrors and turbulent ow eld testing To obtain meaningful PSI data, the phase shifts must occur at a rate that is faster than the changes that are being observed Acousto-optic Bragg cells are the most convenient method to obtain the frequency shifts, and a frequency difference of up to 1 MHz has been demonstrated The interferogram intensity will oscillate at this frequency, and the wavefront phase is encoded in the phase difference of these oscillations at different measuring points Because of the frequencies involved, a high-speed detector is needed; a standard video camera will not work.

This code uses the value of the $mode variable as the operator used to process its two arguments, $a and $b. For example, if you change $mode to * , the code displays 6 instead (2 times 3). In itself this code is rather pointless, but if you can imagine a more complex function, where its contents are determined by external factors such as user input, you can see that it s a potentially powerful feature of PHP. More commonly, you ll use anonymous functions to create callback functions as required by certain built-in functions, as shown in the following example.

With these components as the base, the next two sections provide the software infrastructure for radiation therapy and surgery, respectively. 22.5 THE MULTIMEDIA ePR SYSTEM FOR RADIATION THERAPY TREATMENT 22.5.1 Background

The conceptionally simplest method to collect the data is to use an array of discrete detectors Each will produce an output at 1 MHz with a different phase One detector is de ned as the reference detector, and the phase of the.