Polar Projection and X-Y Omnidirectional Images

© Copyright 1978, 1981, 1985, 1997. Jeffrey R. Charles. All Rights Reserved.

The left image was taken from the center of an intersection with the prototype axial strut "Cassegrain" wide angle reflector which utilized an aspheric metalized plastic L'eggs egg. The angle of view is nearly 320 degrees and the central obscuration is 75 degrees. Panoramic overage is from about 70 degrees below the horizon to 52 degrees above. Some of my axial strut reflectors will cover even more - over 70 degrees above and below the horizon. The aspheric primary reflector points away from the camera, but its coverage is so wide that my fingers, elbows, and even parts of the camera appear on both sides of the image! (The newer Versacorp Omnirama T11 axial strut wide angle reflector has a larger diameter than this early prototype, allowing it to better "see around" the camera and photographer.) Note that the zenith is not at the center of this image, which was taken with a hand held camera having no level indicator. The ability to utilize hand held images which may be taken in more remote locations is why it is desirable to have software which can compensate for pointing errors. Uncorrected, this error will cause the horizon to be curved in a converted panoramic image. The right photo simulates the appearance of a "raw image" produced by the OmniLens. Note the absence of a central obscuration - a feature possible only with the OmniLens. In order to prevent obstruction of the subject by the photographer, the OmniLens should be used with a camera having a self timer or remote release, with the photographer either crouched under the tripod or at a good distance from it. The cost of the OmniLens can be lower if its coverage is limited to 320 degrees or so.

These images are digitally "unwrapped" versions of the above left circular image. The left rectangular image was made by simply using the "Polar Coordinates" filter in Adobe Photoshop, then normalizing the vertical proportions with the "Scale" command. Note the curved horizon which results from the camera not being pointed exactly straight up. The pointing error was corrected in the right image by decentering the circular image so that the horizon was as close to concentric with the center as possible, then all of the steps used for the left image were simply repeated. The horizon circle becomes elliptical when the camera is not pointed straight up, so this process is not a perfect solution; but it certainly is a simple one. The entire process took only a few minutes, but it could all be automated with the right software. The wide dark area at top center is from the decentered central obscuration of the axial strut reflector - not a problem with the OmniLens! The "unwrapped" image can be made longer than 360 degrees (in order to have overlap) by simply making a copy of the round image, rotating it to an angle which corresponds to the desired amount of overlap, then converting it to a second image strip which can be merged with the first. Rotation angles divisible by 90 degrees are recommended when it is necessary to maintain the highest possible resolution.

While it looks like an ordinary fisheye picture, the left image covers nearly 360 degrees and has no central obstruction. It also has minimal radial compression of the subject near the edge of the picture, allowing all areas of the image to contain adequately detailed information. The OmniLens will produce this type of image. The object extending toward the lower right is the edge of a door which is actually behind the optical system! The image was taken in 1978 by attaching a spherical reflector to the edge of the door and photographing it from across the room with a 400 mm lens. The Photoshop "speherize" filter was used in negative mode to reduce the radial image compression. The spherize filter can cause some loss in resolution. The right image shows a simulated "full frame" 360 degree image such as that possible with the OmniLens if it is made with zoom capability. A standard 180 degree fisheye lens would only cover a circle having a diameter slightly smaller than the short dimension of the picture.

This 360 degree composite panoramic image of 12,713 foot Hallett Peak in Rocky Mountain National Park shows the type of dramatic vista which can only be captured in a panorama having a wide vertical coverage. The vertical coverage of this image is over 120 degrees - an easy task with the OmniLens. A circular polar projection image can be converted to a rectangular format in the darkroom or with software.

© Copyright 1978, 1981, 1985, 1997. Jeffrey R. Charles. All Rights Reserved.

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