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The more we can allow for any possible outcome in the markets, the easier it will be for us to quickly admit when we are wrong and thereby accept small losses, let large winners run, and adapt to whatever the market is currently showing as its reality and truth The market has the potential to accelerate psychological and spiritual growth because it forces us to relinquish illusions and embrace the everchanging nature of reality A close friend and longtime colleague, Richard Hom, goes so far as to call participation in the markets reality therapy In many arenas of life, illusions can be nurtured and coddled indefinitely In the markets, however, illusions of being right are punished mercilessly and relentlessly until abandoned in favor of reality1 Many careers never force us to admit our failures or accept responsibility for errors.

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Once the required phase is computed, its implementation in the case of a AWG can be done by choosing the length of each waveguide to yield the required phase This is the way it is already done with the regular PHASAR devices with only the linear grating phase modulation in confocal or Rowland geometries The method is rst discussed below for illustration purposes with respect to a planar geometry, meaning that the phased array apertures are placed on a plane (line for the 2-D case) Generalizations of the results to confocal, Rowland and 3-D geometries are given in the subsequent sections.

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The method is based on rst randomly choosing the locations of the centers of radiating apertures and then either by creating the negative phase of the phasefront (possibly plus a constant) at the chosen locations so that the overall phase is zero (or a constant), or slightly adjusting locations of the centers of radiating apertures such that the total phase shift from such a center to the desired image point equals a constant value, say, zero modulo 2p In both approaches, such points will be referred to as zero-crossings In the second approach, they will be referred to as automatic zero-crossings In practice, the sampling points are chosen semi-irregularly as discussed below The total number of zero-crossings can be a very large number, especially in the presence of linear and spherical phase modulation.

Although pursuit of such livelihoods may sound satisfying to the fragile ego, they are intellectual, emotional, and spiritual dead ends We grow through our failures and admission of fallibility; we mature by embracing humility and being nonattached to the results of our actions; we succeed by shattering illusions of control and flowing with the ever-changing nature of reality Can a person succeed as a trader without adopting this seemingly chaotic and unsettling view of the market Of course Because of the market s multidimensional nature, with discipline, determination, and patience people can adapt to one level of its truth and enjoy a certain degree of suc-.

Practical implementations allow only a small number of apertures, for example, 300 being a typicalnumber in the case of PHASARS In order to avoid the problem of too many apertures, and to avoid harmonics generated due to regular sampling [Ishimaru, 1962], [Lao, 1964], we choose irregularly sampled sparse number of apertures One way to determine zero-crossing locations is given below as a procedure Step 1: The aperture points are initialized by choosing one point at a time randomly along the phased array surface.

In order to achieve this systematically on the total surface of the phased array, the following approach can be used: Initial point locations uniformly spaced point locations small random shifts Step 2(a): If the method of creating the negative phase of the phasefront at the chosen locations is used, the said phase is created physically, for example, by correctly choosing the lengths of the waveguides in the case of PHASAR devices Step 2(b): If the method of automatic zero-crossings is used, correction values are calculated for each of the initial points generated in step 1 to nd the nearest zerocrossing points as Final locations of zero-crossings Initial point locations from step 1 correction terms The two approaches work similarly Below one algorithm to calculate the correction terms to generate the automatic zero-crossings is discussed..

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