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Wavefront coding slims down imaging systems

12 Dec 2006

A new imaging technique known as wavefront coding is helping designers to reduce the cost and weight of imaging systems. Andrew Harvey and Gonzalo Muyo look at how the technique is being applied to thermal imagers used by the military and emergency services.

Image-recovery techniques hit the headlines when they were used to restore early images from the Hubble Space Telescope that suffered from excessive spherical aberration. Today, improvements in the cost:performance ratio of signal processing means that correcting aberrations is now a viable option in very low-cost cameras, even those found in mobile phones.

There is now increasing interest in a technique called wavefront coding that intentionally introduces aberrations prior to the images being restored to diffraction-limited quality. While this may at first appear perverse and more trouble than it is worth, it can reduce both the cost and weight of an imaging system. The advantages of wavefront coding do not end there. The technique also gives the ability to simultaneously obtain large depth of field and high, diffraction-limited resolution. This is important in microscopy for in-focus imaging of biological samples that are thicker than the microscope’s depth of field. It could also be used to increase the depth of field of millimetre-wave personnel scanners.

At the other end of the cost spectrum, wavefront coding offers focus-free imaging for low-cost cameras and an extra degree of freedom when designing ultra-compact lenses for use in PDAs and mobile phones. An additional benefit arises from the fact that the point spread function (PSF) is distributed over several pixels, which reduces the risk of saturation for point-like sources. This feature may increase an image’s dynamic range beyond that of the detector in fields as varied as laser metrology and astronomy.

Adding aberrations

The intentional aberrations are derived by various mathematical methods and have two vital features that enable high-quality image recovery. First, the PSF produced by the aberration should be approximately invariant with respect to specific optical aberrations – the most important of which is defocus. Second, the modulation transfer function (MTF) of the imaging system exhibits no nulls. The most useful type of PSF is extended and asymmetrical – the opposite of the characteristic compact point Airy disc PSF produced by well-corrected optics.

The technique, which is also referred to as PSF coding, is summarized in figure 1 and is analogous to digital communication systems that use codecs. The first step involves the optical convolution of the image with the PSF, which effectively encodes the image. Once the image has been transmitted through an imperfect communication channel of aberrating optics, it can then be decoded and restored using digital deconvolution.

As with digital codecs, it is the control of redundancy that determines the encoding used. In optical imaging, the nulls in a lens’s MTF and the consequent loss of information are caused by the redundancy associated with aberrations such as defocus. In this case, defocus applies the same wavefront distortion across the width of the lens.

This redundancy is efficiently overcome by using antisymmetric phase masks as these exhibit no redundancy. The most effective of these masks have a cubic or generalized cubic form, shown in figure 2 with their in-focus and defocused PSFs.

Although these PSFs look very different to traditional ones, they are almost invariant with respect to defocus. The image recorded at the detector is the convolution of the PSFs shown and the ideal image of the scene. Simple deconvolution of the recorded image yields a sharp image even in the presence of significant defocus as depicted in figure 3. Because the PSFs are invariant to defocus, the recovered image is also invariant to defocus. Similarly, because the MTF exhibits no nulls, the image recovery incurs only modest noise amplification.

The top two images in figure 3 show a spoke target recorded in focus and with severe defocus. Excessive blurring and the well known phase reversal of the spokes in the defocused image are apparent.

The bottom two images in figure 3, which were recorded using wavefront coding, are almost identical in both the in-focus and severe defocus cases. The presence of high-order aberrations, such as coma and spherical aberration also has a greatly reduced impact on the quality of the recovered image. This opens up opportunities for designing simpler, lower-cost lenses that may exhibit significant magnitudes of these aberrations, but can be removed by incorporating wavefront coding into the design process, lowering the overall system cost.

There is of course a quid quo pro. For the highest possible signal-to-noise ratio, the image recorded at the detector should have the maximum possible contrast. However, the coding process clearly reduces the contrast of the detected image. Image restoration recovers a high-contrast image, but also amplifies the noise accompanying detection. Although a high-quality image can be recorded over a wider range of optical aberrations than by traditional imaging, the signal-to-noise ratio will generally be poorer than the best image recorded by conventional means.

Emerging applications

A major application area for wavefront coding is in reducing the cost of imaging systems. One example where this is becoming increasingly important is in the low-cost thermal imaging used by the military and emergency services.

The optics used in thermal imagers are inherently expensive to manufacture. The fast optics required for high sensitivity employ not only multi-element aspheric lenses for aberration control but also infrared transmissive materials such as germanium and gallium arsenide, which are expensive and tend to introduce additional chromatic- and thermal-related defocus. Although these defocus problems can be readily reduced and overcome using wavefront coding, the technique has the greatest impact when it comes to minimizing field-related aberrations.

In collaboration with our partners, QinetiQ, Qioptiq, FLIR Systems and SAAB, we have recently used wavefront coding to demonstrate the first single-element thermal-imaging lens. An imaging system employing this single-element coded lens exhibits image sharpness across a field of view equal to one employing a traditional two-element lens, but with the reduced cost and weight associated with the simpler lens. In this instance, the two-element lens uses a Petzval set-up to flatten the field curvature and astigmatism produced by the front element. In comparison, the coded singlet has a PSF that is invariant to field curvature and astigmatism – even though it varied by up to six waves across the full 7.5° field of view.

Images recorded with this prototype singlet, shown in figure 4, clearly demonstrate the improved sharpness across the final image. Although there is a small increase in noise in the wavefront-coded image, the overall image quality is clearly superior. Crucially, the image quality is sufficient for many military and emergency-service applications.

The role of wavefront coding in this example is to mitigate compromises in optical performance and enable cost and weight reductions. Most imaging systems involve optimization of imaging performance using all available parameters, such as lens shape, element count and the lens material used. An optical/digital codec approach, such as wavefront coding, offers an additional way to optimize overall imaging performance.

• This article originally appeared in the December 2006 issue of Optics & Laser Europe magazine.

Mad City Labs, Inc.LASEROPTIK GmbHFirst Light ImagingAlluxaCHROMA TECHNOLOGY CORP.Berkeley Nucleonics CorporationSPECTROGON AB
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