Spatial Warping Experiments With A Precision CRT Display

AbstractWe have recently assembled a precision CRT display system which uses 16 -bit digital -to- analog converters to control its x and y deflections. We have used this hardware toperform spatial warping experiments with digital images in which the desired locations ofthe pixels are computed according to the warp functions. For moderately distorted images,the cosmetic defects in imagery produced by this process may be acceptable in some of ourapplications. We show that the polynomials describing the warping functions can be effici-ently evaluated by finite difference tables. We discuss the design of microprogrammedcontrollers, which can calculate the warped coordinates at the same rate that the CRT beamexposes the film by using difference tables.IntroductionSolar astronomers at Kitt Peak National Observatory (KPNO) have used a precision cathoderay tube (CRT) for about eight years to record 2048- square, digital, solar magnetogramimages on photographic film('). Recently, the Observatory purchased another CRT withhigher performance to replace the older system in the magnetogram application. We are nowconstructing two identical computer interfaces for these two display systems, and the oldersystem, with a new, improved interface, will soon begin a new life with the InteractivePicture Processing System(2,3) at KPNO. Early in the design process for the new interface,it was suggested that 16 -bit digital -to- analog converters (DACs) might be capable of gener-ating deflection signals that could spatially warp digital images while they are beingrecorded on the film. This paper is a progress report on our investigation of this idea.HardwareBoth of our precision CRT display systems were made by Constantine Engineering Laborator-ies (CELLO). Each contains a CRT with a phosphor diameter of 125 mm. The newer system iscapable of resolving about 4000 pixels across its useful area, while the older systemresolves only about 2000 pixels. We set the desired x and y digital coordinates of a pixelinto the DACs, wait for the beam deflection to stabilize, and finally, gate the constant -current beam for an amount of time proportional to the desired exposure for the pixel. Weare currently using pixel exposure times from 0 to 127 microseconds, but in the final ver-sion of the new interface, we expect to use a maximum time of 51 microseconds, quantized inunits of 200 nanoseconds.Most of our efforts in the design and construction of the new interface have gone intotrying to satisfy the requirement to generate clean, precise analog deflection signals. Weare using Datel model HR16B DACs to generate the precision deflection voltages. We areusing optical isolators on all digital connections to the computer system, and have paidcareful attention to details of layout in the analog portions of our circuitry in an effortto avoid ground loops and noise which could degrade the performance of these 16 -bit DACs.The DACs have three trimming potentiometers which are associated with the three dividerchain resistors controlled by the most significant bits of the 16 -bit digital input. Wehave adjusted these "trimpots" so that each DAC produces a smoothly- stepped analog outputas the digital input word steps through transitions of these bits. We have also measuredthe error in the fourth bit of each DAC and have installed an external, fixed trimmingresistor to correct it. Transitions of worst -case combinations of bits of lesser signific-ance may still be preventing achievement of monotonicity in the 16th bit. We believe thatfurther trimming improvements are certainly feasible. These efforts are important becauseerrors in DAC output imply errors in positioning of the pixels in the film image, and quitesmall pixel spacing discrepancies can become painfully obvious when they systematicallyaffect whole rows or columns of an image.Spatial WarpingWe thought of spatial warping soon after we realized that the 16 -bit DACs would allow usto position the CRT electron beam in units of a fraction of the beam width. The resolutionof the DACs corresponds to about 1 /16th of the beam width of our older CRT and to about