Unified Optical Scanning Technology

Chapter 3 - Scanned Resolution

3.1 INFLUENCE AND SIGNIFICANCE OF SCANNED RESOLUTION

In the earlier chapters, a few key items were introduced that were to be expanded here. They include the resolution invariant of Section 1.4, the aperture shape factor of Section 2.1.2, and the Gaussian spot size of Section 2.3.2. This chapter develops scanned resolution for general application. The exposition of this subject before concentrating on the scanning techniques underscores its basic independence from any specific methods of deflection or system architecture.* Furthermore, it may be appreciated that the resolution of a scanning system can be calculated straightforwardly, avoiding diversion by potentially complicating system factors.

3.1.1 Basis of Scanned Resolution

Various technical communities apply the word "resolution" differently. In astronomy, it means the limiting small angle that subtends two observed remote objects (in fractional arc seconds or microradians).

In photographic imaging, it means the largest number of spatial cycles countable in one millimeter of the information medium (in cycles or line pairs per millimeter). Television technology departed from the above 'limited field" descriptors by accounting for the effort expended (in electronic image capture and display and in signal bandwidth), by defining resolution as the total number of picture elements (pixels or lines) conveyed in one scan direction of a total field. Television also counts two pixels per information cycle. This general philosophy is sustained in optical scanning, representing the achievement of full field resolutions that can extend into the tens of thousands of information elements per scan. Certain scanning systems (to be described) can convey 100,000 or more elements per single scan. Usually, the scanned spatial path is effectively linear and traversed at relatively uniform velocity, encompassing data elements that are nominally equally spaced. Scanned resolution is represented by the letter N.

Two fundamental forms of optical scanning, translational and angular, can exist independently or jointly. Exemplifying these options with a laser beam, translational scan displaces a focal point of spot size δ over a format length S (as by movement along a collimated beam axis of a "pick-off" mirror coupled to a focusing lens). Assuming that elemental spacings correspond to the spot size δ, the resolution of translational scan Nsis expressed by

Angular scan is achieved by nutating a beam that is ultimately con-verged to focus, such that the locus of its focal spots δ traverses a format width W. Again assuming that elemental spacings correspond to the spot size δ, the resolution of angular scan NΘmay be represented similarly by

An equivalent angular relationship, introduced in Section 1.4, is given as the ratio of the full active scanned angle Θ to the diffracted angle ΔΘ. This is analogous to the basic expression for (electrical) signal-to-noise ratio; the ratio of full signal S to the uncertainty in signal ΔS.

* An extensive discussion of scanned resolution appears in Section 2.8 of Holographic Scanning (Beiser, 1988), deriving and illustrating several aspects of the topic presented here.

Similarly for pointing accuracy or small angle "staring" (Section 4.5.4), where the descriptor "finesse" is appropriate.

 

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