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Updated: January 12th, 2011 09:49 AM CDT

Achieving Optical Zoom Via Optical Distortion

Inexpensive optical zoom capability that can approach digital still camera quality remains compatible with the compact modules required for portable electronics
Figure 1
© Tessera Technologies
Figure 1: Total number of pixels that contain information (before interpolation) in a zoomed-in image by a magnification factor of M.
Figure 2
© Tessera Technologies
Figure 2: Information (percentage of total information in original image) contained in a zoomed-in image as a function of the zoom magnification factor.
Figure 3
© Tessera Technologies
Figure 3: Point spread function of an on-axis point source. The PSF on the right is measured for an optical system comprising three plastic lenses lens (linear scale).
Figure 4
© Tessera Technologies
Figure 4: Point spread function of an off-axis point source for angle of incidence of 25°. The PSF on the right is measured for a 3P lens system (linear scale).
Figure 5
© Tessera Technologies
Figure 5: Two types of distortion schemes: (a) Rotationally symmetric distortion. (b) Anamorphic distortion.
Figure 6
© Tessera Technologies
Figure 6: Transformed pixels positions in case of unit magnification. Blue region consists of the pixels that finally restore the whole FOV. (a) Distorted pixels positions; (b) Corrected pixels positions. The rectangle provides the sensor size.
Figure 7
© Tessera Technologies
Figure 7: A typical relative illumination curve
Figure 8
© Tessera Technologies
Figure 8: The ratio of the number of pixels, required for lossless zoom, with respect to the number of pixels that cover the whole FOV in a standard system with no zoom capability for discrete zoom steps and for continuous zoom
Figure 9
© Tessera Technologies
Figure 9: Colored scene captured with a prototype of the zoom lens and processed to correct distortion (only middle field is shown). (a) image before distortion correction; (b) image after distortion correction with 1X optical zoom magnification; (c) image after distortion correction with 2X optical zoom magnification.
Figure 10
© Tessera Technologies
Figure 10: Magnified text at 2X zoom captured with: (a) a 2MP DSC with a digital zoom. (b) a 2MP camera that uses a lens prototype based on OptiML™ Zoom technology.
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By Eyal Ben-Eliezer and Noy Cohen, Tessera Technologies, Inc.

Most camera phones that provide zoom capability do so through digital zoom. Digital zoom is accomplished by cropping an image and interpolating the result back to the original frame dimension. Restricting the field of view in this manner gives a perception of magnification. Although inexpensive to implement, the digital zoom degrades resolution and detail compared to optical zoom solutions, where the focal length of the optical system is dynamically varied. Typically, this change in focal length is accomplished through a mechanical shift in the position of one or more lenses. However, optical zoom solutions tend to suffer from slow operation and vulnerability to mechanical damage and are often physically large, power hungry and expensive. This article proposes two new approaches to optical zoom, differentiated by the magnification they provide.

The first, for standard-range zoom applications, is based on a fixed-focus, distorting lens that provides variable magnification across the image sensor. The second approach consists of a dual-state mechanical assembly in conjunction with a distorting lens to provide continuous extended-range zoom. In both cases digital restoration corrects distortion of the captured image. Such approaches provide inexpensive optical zoom capability that can approach digital still camera quality but are compatible with the physically compact camera modules required for portable electronics products. Being purely an optics/software solution, it is suitable for all imager technologies and all resolutions from QCIF to >10Mpixel. Consequently, broad adoption of these new zoom solutions on camera phones is expected in the near-term.

Optical zoom allows the user to artificially "get closer" to a distant object. Magnification is achieved by restricting the field-of-view (FOV) and increasing focal length, making it possible to capture a distant scene without loss of resolution. Most commercial digital still cameras (DSCs) provide optical zoom capability.

Zoom lenses commonly used in most DSCs are composed of three to five groups of lenses1-2. Mechanical shift of those groups with respect to each other varies the focal length while maintaining image sharpness on the detector. To artificially get closer to a distant or a small object, the focal length is increased. Since the detector size is fixed, the resulting image magnification is associated with a decrease in the FOV.

Since 2001, cell phones have been equipped with cameras. Cell phones impose severe constraints on the optical design of camera modules, since the component cannot exceed a dictated height in order to fit within the thickness of the camera phone body. Most common lens assemblies are made of two to four mostly plastic elements, which are fixed in position. Moreover, the optical assembly needs to be as inexpensive as possible, owing to the severe price sensitivity of this market segment. Therefore, mechanical zoom lenses are out of the question in low- to mid-range priced cell phones.

High-end cell phones tend to be physically thicker and sell more on features, styling and brand than raw price. This has made it possible for some high-end cell phone makers to incorporate optical zoom, implemented by mechanical means. For example, small piezoelectric motors are able to provide movement in the "Z" direction, allowing a complete lens assembly with zoom to be accomplished in a length of approximately 15mm. However, the issue of robustness has not been satisfactorily solved. Another less common approach is to use liquid lenses. Such lenses change their focal length when pressure or electrostatic force is applied to the liquid inside the lens. Since the image needs to remain sharp on the detector, at least two lenses of this type are required. Significant pincushion distortion and chromatic aberration exist in fluid lenses and they further suffer from low durability and mechanical-fatigue that reduce performance over time.

Digital Zoom

Most cell phone cameras utilize digital zoom. A central portion of the image is cropped and increased to restore the size of the image to the original detector size. Since the number of pixels remaining is smaller than the number of the pixels in the whole detector area, interpolation is used to restore the image size³. The result is an image of the same size as the original, but with a smaller FOV and thus seems magnified. However, digital zoom degrades the image resolution since the original detail is spread over a larger area by interpolation.

Many different methods have been devised to accomplish the interpolation. The simplest is the nearest neighbor, where pixels are just duplicated. Bi-linear and bi-cubic methods use a simple average to predict the value of a missing pixel. There are other more sophisticated schemes that provide better results, albeit with the penalty of higher computational effort. In cell phones, intensive computation is undesirable since it directly impacts battery life.

The amount of information contained in an image is proportional to the number of the pixels that make up the image. Let us assume a sensor with 3 megapixels, arranged in 1536 rows by 2048 columns and that a digital zoom of 2X is required. First, the scene is captured regularly, i.e. the whole FOV covers the detector. Then the image is cropped, leaving a central portion of half of the rows and half of the columns (i.e. 768 rows and 1024 columns) to which interpolation is applied. The amount of information in the zoom image is dictated by the size of the portion that is left from the original image. Since only one quarter of the original image is used for the interpolation, only one quarter of the original information remains.

Consider an image with y rows and x columns where digital zoom magnification of M is applied upon by cropping, and where the central portion of the image that has y/M rows and x/M columns is retained and interpolated, as shown in Fig 1.

Thus, the number of pixels in the zoom image is inversely proportional to the square of the digital magnification. Expressed another way, the information contained in a digitally zoomed image is the information of the initial image divided by the square of the magnification. This is illustrated in Figure 2.

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