1. Introduction

An annular aperture can be used in a telescope to suppress the contributions of the lower spatial frequencies in an image compared to a full aperture while maintaining the high spatial frequency response. As such, images taken with a telescope having a large central obscuration show enhanced contrast at the highest spatial frequencies [1]. The penalty for a large obscuration is extreme light loss and reduced contrast in the image due to a higher percentage of light shifted into the Airy Rings. To compensate for this light loss the exposure time can be increased, although this is at the expense of temporal resolution. Unfortunately in some imaging systems, astronomical telescopes with atmospheric turbulence as an example, long exposures result in smeared out images due to degraded image stability.

Achieving the goal of obtaining high-resolution images by suppressing the low spatial frequency response requires that large obscurations and increased exposures be combined within a single imaging system. This can be accomplished by directing the low spatial frequency light into a tip-tilt sensor and, using a fast steering mirror [2] for image stabilization, recording the high spatial frequency light separately using an appropriate exposure time.

In this letter, we present a concept for a compact, stabilized, high resolution imaging system.

2. High spatial resolution imaging

One of the challenges in developing optical feedback systems to be used for imaging faint objects is to avoid sharing the object’s light between the imager and the control sensor in a way that degrades the system’s overall performance. When imaging bright sources, this is not as much of an issue and combinations of beam splitters and dichroic optics have been successfully used. An example of this is the pupil masking experiment using the sun [3], which used 3 beam splitters to share the light among four independent camera systems. Using a bright source, this work successfully showed that the contrast of the high spatial frequency information could be enhanced in a telescope with a large central obscuration.

Several authors (see references contained in [4]) have discussed the use of an annular aperture to increase the contrast in the high spatial frequencies. Figure 1 shows a 2-dimensional cut through the optical transfer function (OTF) of a telescope having a 15% and an 87.5% obscuration. The right image illustrates that there is a pronounced suppression of the contributions from the lower spatial frequencies when using a large obscuration. This idea has been extended to the use of variable transmission across an aperture by introducing gradient apodization, for example, in ref [4].

 

Fig. 1. Plots of the normalized optical transfer function for a regular telescope (15%) and one with a large (87.5%) central obscuration. Notice in the large obscuration case (right) that the contributions of the lower spatial frequencies are suppressed compared to the regular telescope (left).

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A related issue, and an application of the imager in this paper, is the problem of low spatial frequency light contamination in images. Recent work on ground-based imaging of the planet Mercury [5] suffered from the light from the bright, extended surface of the object reducing the visibility of the smaller scale features. In this case short exposures were used and high fidelity CCD images selected and combined to investigate the surface features of the planet. A desirable improvement to this technique would reduce the background low spatial frequency information while enhancing the high spatial frequency information.

The problem of sharing the light to be used for imaging and low-resolution light contamination can be minimized or eliminated by optically separating out the light to be used for imaging. This can be effectively accomplished using pupil masking, in this case introducing a larger obscuration, and redirecting the light intercepted by the obscuration to an image stabilizer.

3. Active imager

The most straightforward approach to synthetic aperture imaging is to use a transmissive annulus in the pupil of an optical system. In a telescope this annulus can be placed at the primary aperture stop. The disadvantage to this is that it is typically the largest physical aperture in the system and that the light blocked by the opaque portions of the mask remains unused. We can improve on this by re-imaging the telescope pupil elsewhere in the system at a smaller size and splitting off a portion of the light to be used for image stabilization.

Introducing an elliptical mirror as the inner surface of the annulus at a 45° angle to the incoming beam effectively splits the light from the re-imaged pupil into two separate beams. The central portion of the incident light is then redirected onto the sensor of an image stabilizer, while the tip-tilt corrected annulus of light is allowed to pass by the mirror and is brought to focus on the imaging camera. Such a system can be constructed using only reflective optics to minimize the transmission losses associated with refractive optics thus providing an efficient means of imaging faint sources.

4. Discussion

The strength of this type of imager is demonstrated in Figure 2, which shows its application to an image of the moon. From left to right the figure shows a raw or truth image, next the raw image convolved with an OTF with a 15% obscuration and atmospheric blurring, and finally an annular OTF (87.5% obscuration) with the atmospheric jitter removed.

The difference in the intensities between the convolved images is due to the difference in the amount of light that passes through the two OTFs. One of the goals in the development of this imager is to suppress the bright, low spatial frequency component of the target being imaged. This desired effect is clearly seen when comparing the two convolved images.

 

Fig. 2. Image of the moon from left to right showing a truth image, the truth image convolved with a 15% obscured telescope OTF with blurring similar to that caused by imaging through the atmosphere and the truth image convolved with an 87.5% obscured telescope OTF with image stabilization.

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In this discussion, we have restricted the aperture shape to being circular, however, there are advantages in considering other aperture shapes. In particular, the use of a square aperture can have significant advantages for controlling the telescope’s diffraction effects [6]. In imagers being used for double star work and operating close to the diffraction limit, a faint companion can be obscured by the Airy ring pattern. Using a square aperture the focal surface would show a two-dimensional “sinc function”, which could provide additional leverage for separating out the two stars.

Figure 3 shows the increase in the exposure time required to maintain the signal to noise ratio as a function of the obscuration (taken as the ratio of the inner to outer diameter of the annulus). The angular resolution of the system is set by the outside diameter of the annulus and the width of the annulus defines the range of spatial frequencies sampled. Clearly, the need for image stabilization increases with the exposure time to maintain the image quality.

The fast steering mirror and tip-tilt sensor requirements for this imager are very modest. Since there will be a significant fraction of the object’s light directed to the stabilization system to correct for the lowest optical modes this imager will work well with faint sources. Correction rates of less than 100Hz will provide very effective stabilization over a broad range of atmospheric conditions and commercial systems of this type are readily available. One drawback to this system is that it cannot be easily adapted to diffraction limited imaging. The light that is used for imaging passes through the annulus and is not available for sampling by a wavefront sensor making it difficult to correct residual wavefront errors. However, some correction for lower order wavefront errors should be possible by replacing the tip tilt sensor with a wavefront sensor and using an optical element that can be deformed modally.

 

Fig. 3. The factor that the exposure time must be increased as a function of obscuration, normalized to a 15% obscured OTF. For an 87.5% obscuration about 25% of the light gets through requiring an exposure of about 4 times as long to obtain the same signal-to- noise ratio. This represents the worst-case scenario as the desired signal to noise ratio of the spatial frequencies of interest could be met in less time.

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5. Summary

We have described a system for obtaining high-resolution images by increasing the contrast in the high spatial frequencies by combining an aperture mask with large obscurations and a fast steering mirror. By varying the diameter and width of the annulus, the upper limit of the spatial frequencies and the range of frequencies, respectively, can be selected. An additional feature of this imager is that the shape of the aperture mask is not limited to that of a circle and can be modified to take many different shapes to accommodate a preferred diffraction pattern.