Advanced Imaging


Advanced Imaging Magazine

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.

By Eyal Ben-Eliezer and Noy Cohen, Tessera Technologies, Inc.

Symmetry Considerations

In an optical system, there usually is the flexibility to select the system symmetry in a way that fits the functional requirements and product cost. For most cases rotational symmetry is the most appropriate. However, for a system that provides zoom by optical distortion and where the image sensor is rectangular, anamorphic symmetry has advantages. When the distortion in the x axis is independent of the distortion in the y axis, simpler distortion correction may be applied, reducing the processing and memory requirements. Examples of rotational symmetry distortion as well as anamorphic distortion are presented in Figure 5(a) and Figure 5(b), respectively.

Sampling Rate Considerations

Figure 5 reveals that careful consideration should be given to the sampling rate in the image boundaries. Because the image is distorted in such a way it is magnified at the center of the FOV, while being compressed at its boundaries, if no information loss is allowed, the boundaries will determine the sampling rate.

Consider the case in Figure 8, where P discrete magnification steps are assumed. Z1 is the highest magnification, since it is in the center of the FOV and the magnification values monotonically decrease toward the smallest magnification value, Zp. As those discrete steps become continuous, the ratio between the number of pixels required for lossless zoom, with respect to the number of pixels, N, that covers the whole FOV in a standard system with no zoom capability becomes logarithmic. Therefore, as the maximum magnification increases, the number of pixels that are required for continuous lossless zoom for the whole image increases as well.

To have a lossless and continuous zoom up to a magnification of Zmax in a standard imaging system for the whole FOV it would require NZ2max pixels, where N is the number of pixels that cover the whole FOV in a standard system with no zoom feature. The number of pixels required using the approach of optical distortion, with respect to a standard imaging system provides a major improvement, since a logarithmic function increases slower than a parabolic one. As an example, to obtain lossless 2X continuous zoom for the whole FOV, with a quality of 2M pixel sensor, one needs 8M pixels if a standard simple lens is used but only 4.77M pixel when an optical distortion lens is used.

In most cases, the information that is applicable for the application of zoom is located in the center of the FOV. This is advantageous for an optical distortion zoom approach since the information in the borders is sacrificed and the number of the pixels that are required to obtain a high-quality, zoomed image in the center of the FOV becomes much smaller. Fortuitously, these pixels also contain more information compared to a standard imaging system having digital zoom. Likewise, when a 1X image is required, extra image information in the center of the image is discarded.

Extended-Range Optical Zoom System

One of the weaknesses of conventional optical zoom systems is the need to have complete control of the position of each lens through its range of travel. A more robust solution is to move the lenses between stops, but the magnification then changes in fixed intervals. Continuous high magnification can be achieved with a hybrid approach where a zoom lens system that works by optical distortion and digital correction is shifted mechanically between discrete positions. In doing so, the zoom capability is increased even further while maintaining a simple mechanical assembly. For example, consider the case of two discrete mechanical states with a continuously variable zoom range in each state. One state will have a generally larger zoom range (and smaller FOV) than the other. The zoom ranges in the discrete states may or may not overlap. Where the ranges do overlap, this solution provides continuous zoom capability over a contiguous, extended range. The digital restoration discussed earlier is applied in both mechanical states to provide the final, undistorted output image for any required zoom value within the zoom range.

Experimental Realization

A standard 2MP DSC was modified so that the optical train provided the desired optical distortion. All processing was done on bitmap images after the whole standard image sensor processor pipeline. Digital zoom was synthesized using bicubic-spline interpolation (not all the FOV is shown). Figure 9(a) shows a distorted color scene, captured by the camera before digital correction. The outputs with 1X and 2X optical zoom magnifications, after digital correction, are shown in Figure 9(b) and Figure 9(c) respectively.

Comparison between outputs for a 2X zoom magnification of textual information, captured with a 2MP DSC with a simple digital zoom, as well as with a camera that uses the prototype optical distortion lens are presented in Figure 10(a) and Figure 10(b), respectively. Comparing the 2X optical and digital magnifications, there is a noticeable improvement in resolution for the optical approach over a standard system.


The performance of cameras in cell phones is advancing rapidly toward that which already exists in DSCs. The constraints on achieving parity in image quality are price, size and reliability. Consequently, zoom lenses that change magnification by the traditional method of mechanical displacement of optical surfaces are unsuitable for this application.

A new approach to achieving optical zoom is by a fixed-focus lens that distorts the image in such a way that the central FOV region is magnified, while borders are compressed. This facilitates standard-range optical zoom without requiring moving parts or complex mechanical systems. By combining this with a simple dual-state mechanical assembly, extended-range zoom capability can be realized. To retrieve an output image that is not distorted, post-processing for distortion correction is applied. The tradeoff between the required zoom and sensor resolution has been presented and analyzed. This method of zoom is shown to provide a major saving in pixel resolution requirements with respect to a standard system.

The performance of a phone camera that uses an optical distortion zoom lens is higher than one using digital zoom. The image contains more information while the computation effort remains almost the same. Therefore, this new approach provides a unique, inexpensive and novel solution to providing the optical zoom feature, while meeting the price, size and reliability constraints of cell phone cameras.

Eyal Ben-Eliezer is Project Leader at Tessera Technologies, Inc., and Noy Cohen is Algorithms and SW Team Leader at Tessera Technologies, Inc. The authors wish to thank Gal Shabtay, Vice President, Research and Devleopment, Ephraim Goldenberg, Optics Team Leader, and David Mendlovic, General Manager, Tessera (Tel Aviv, Israel) for their contributions to this article.


  1. Kingslake, Rudolph, Lens Design Fundamentals, Academic Press, 1978.
  2. Clark, A.D. (1973), Zoom Lenses, Monographs on Applied Optics No. 7. Adam Hildger (London).
  3. W. K. Pratt (2001), Digital Image Processing, John Wiley & Sons, (Third Ed)
  4. OptiML™ Zoom. Tessera
  5. See e.g., International Patent Application No. PCT/EP2006/002861 (published 04 October 2007 as WO/2007/110097)

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