Defocus Correction Research Articles

Effect of rotation and translation on the expected benefit of an ideal method to correct the eye's higher-order aberrations.

An ideal correcting method, such as a customized contact lens, laser refractive surgery, or adaptive optics, that corrects higher-order aberrations as well as defocus and astigmatism could improve vision. The benefit achieved with this ideal method will be limited by decentration. To estimate the significance of this potential limitation we studied the effect on image quality expected when an ideal correcting method translates or rotates with respect to the eye's pupil. Actual wave aberrations were obtained from ten human eyes for a 7.3-mm pupil with a Shack-Hartmann sensor. We computed the residual aberrations that appear as a result of translation or rotation of an otherwise ideal correction. The model is valid for adaptive optics, contact lenses, and phase plates, but it constitutes only a first approximation to the laser refractive surgery case where tissue removal occurs. Calculations suggest that the typical decentrations will reduce only slightly the optical benefits expected from an ideal correcting method. For typical decentrations the ideal correcting method offers a benefit in modulation 2-4 times higher (1.5-2 times in white light) than with a standard correction of defocus and astigmatism. We obtained analytical expressions that show the impact of translation and rotation on individual Zernike terms. These calculations also reveal which aberrations are most beneficial to correct. We provided practical rules to implement a selective correction depending on the amount of decentration. An experimental study was performed with an aberrated artificial eye corrected with an adaptive optics system, validating the theoretical predictions. The results in a keratoconic subject, also corrected with adaptive optics, showed that important benefits are obtained despite decentrations in highly aberrated eyes.

Improved performance of adaptive optics in the visible

A simple tip–tilt adaptive optics system can improve the peak intensity of the corrected image in the infrared by a factor of 2 to 3 compared with that of the uncorrected image. With conventional methods this performance cannot be achieved in the visible unless flexible mirrors are used. A method of improving the peak intensity in the visible by a factor of 8 to 10 compared with that of the uncorrected image by use of a simple tip–tilt mirror is presented. To achieve this improvement, the effective wave aberration, that is, the aberration modulo 2π, is used to obtain tilt and defocus of the turbulent wave front. It is shown that correcting the effective aberration is the equivalent in Fourier space of shift-and-add in image space, that is, moving the brightest speckle to the image center. Christou [ Pub. Astron. Soc. Pac.103, 1040 ( 1991)] has demonstrated the potential of a tip–tilt system when using shift-and-add. Operating in Fourier space rather than in image space offers the advantage of being independent of the type of object to be used for the correction. Additionally, this method is applied to the correction of defocus by determination of the brightest speckle in the three-dimensional image space. Thus the full potential of a rigid-mirror adaptive optics system is demonstrated.

Defocus Correction Using a Visibility Criterion

Abstract Michelson visibility is used to identify areas of correct focusing in stacks of images with progressively severe defocusing. It is found that visibility is a maximum when focusing is correct. An image with partially corrected defocusing is constructed using this criterion.

Analysis of laser beam quality degradation caused by quartic phase aberrations

Simple formulas are derived for the degradation in the beam-quality factor, M(2), of an arbitrary laser beam caused by quartic phase distortions such as those that might occur in a spherically aberrated optical component, a thermally aberrated laser output window, or a divergent beam emerging from a high-index dielectric medium as in a wide-stripe, unstable-resonator diode laser. A new formula for the defocus correction that is needed to collimate optimally a beam with quartic phase aberration is also derived. Analytical results and numerical examples are given for both radially aberrated and one-dimensionaltransversely aberrated cases, and a simple experimental measurement of the beam-quality degradation produced by a thin plano-convex lens is shown to be in good agreement with the theory.

Practical autoalignment of transmission electron microscopes

We present a working method for automatic correction of beam misalignment, defocus and objective lens astigmatism based upon computer-induced beam tilts which result in image shifts that are measured and used to adjust the microscope. The performance of the method has been tested on 100 and 400 keV microscopes, and it proves to work reliably over a wide range of magnifications for both weak phase and amplitude contrast specimens. The performance of the alignment procedure is instrumentation, specimen and magnification dependent. The reproducibility for alignment on the coma-free axis was measured to be less then 0.1 mrad at magnification M = 500 000 and less then 2 mrad at M = 10 000. The reproducibility for focusing and stigmation was measured to be less then 3 nm at M = 500 000 and less then 50 nm at M = 10 000.

Absolute astigmatism correction for flat field spectrographs

Absolute astigmatism correction for flat field spectrographs is possible over an arbitrary wavelength range, while absolute defocus correction is not possible.

The on-line use of histogram data for high-speed correction and alignment of electron microscope images

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

The effect of x-ray linewidth on the defocus correction in the Schulz reflection technique for texture measurement

The loss of measured intensity with increasing specimen inclination in the Schulz reflection technique for texture determination is due to the increase in the width of the diffracted beam profile with increasing inclination. This increase in width is relatively greater for a sharp rather than broad profile. Since the metallurgical condition affects the width of the profile, it also affects the defocus correction. To make an accurate texture measurement one must determine the defocus correction using a specimen of random texture which has a diffracted beamwidth similar to that of the material of interest.

Partial Defocus Correction by Defocus of a Coherent Optical System*

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text T. M. Holladay and P. G. Roetling, "Partial Defocus Correction by Defocus of a Coherent Optical System*," J. Opt. Soc. Am. 59, 460_1-462 (1969) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article