ECEN 4616/56163/6/2013

Strehl Ratio:

The Strehl Ratio (named after German physicist Karl Strehl, 1864-1940) is a measure of optical quality for optical systems that are fairly well corrected. It is a one-number measure of the quality of an optical system.

An (circularly-symmetric) optical system with no aberrations produces a PSF that is the Airy Pattern:

When a small amount of spherical (or other) aberrations are present, the energy in the peak of the PSF shifts to the rings:

The two PSFs (unaberrated and aberrated) look similar, and both even have reasonable MTFs:

No Aberration: Sph Aberration:

However, a profile plot through the PSF shows that the power in the peak of the Airy pattern is significantly reduced:

The Strehl Ratio is defined as the ratio of the peak of the actual PSF compared to the peak of the ideal (unaberrated) Airy pattern. The Strehl ratio for this aberrated PSF is reported (by the Huygen’s PSF analysis window) as 0.720:


There is an operand (“STRH”) for the Merit Function Editor which returns the Strehl ratio for a given combination of configurations, wavelengths and field.

Optimizing the strehl ratio is a useful way of refining optical systems, since it reduces the complexities of 2D wavefront errors (and MTF values) into a single number. Since the merit function requires the merit of a trial system to be a single number, the Strehl ratio is an easy way to get there.

It is relatively simple to measure the Strehl ratio, if at least part of the object is a point source. Hence, for astronomical imaging, the Strehl ratio can be used to detect a “Lucky Imaging” situation.

A rough design for an amateur “Lucky Imaging” telescope system:

The lucky image detector can be as simple as an x-y adjustable pinhole which is centered on a guide star, with a single detector behind. When the intensity passed through the pinhole exceeds a set amount, the detector is set to integrate – when the power level falls, the detector is turned off. This would remove both tip-tilt errors and de-focus errors, at the expense of only integrating for a fraction of the observing time. A tip-tilt correction mirror would allow an increased fraction for detection time.

A common way to get increased resolution in small telescopes today is to use a video camera to take many thousands of pictures, then use computer algorithms to align and sum the images. It is interesting to imagine how these algorithms might be improved:

  • Before summing an image, “nearby” star images might be scanned to estimate the Strehl ratio, and only use images with sufficiently high values. This might require that the PSFs be slightly oversampled, as we want to find the power in the central peak, and not integrate over the rings as well.
  • Papers (and research) have discovered that summing images over a range of focus produces effective PSFs that are invariant over a significant range of focus and have no zeros in the MTF. Thus, summed images can, in principle, be filtered to achieve effective diffraction limited images. (Or even beyond diffraction limited, due to the “Lucky Imaging” effect.)

Both these methods could be simulated (in Matlab and/or Zemax) and their effectiveness estimated.

Scheimpflug Principle:

Consider the problem of taking a picture of the top of a table, from an oblique angle:

Only a portion of the table-top will be in focus. The resulting image would look something like this:

Is there some way to achieve a focal plane and DOF like this:

The problem is solved by a camera type known as a “View Camera”:

While this simply looks like an antique camera, it is not. (Although there are antique view cameras, they are also produced today.) The defining characteristic of a view camera is its ability to move the lens with at least 3 degrees of freedom (x,y tilt, and z translation):

How does this help? Consider the imaging properties of a lens if the object is tilted:

When the tilted object is in focus, the focal plane, image plane and lens plane have the characteristic that they intersect at a line:

This is known as the “Scheimpflug Condition”.

For a derivation from paraxial optics, see:

The Scheimpflug principle also works with afocal systems, allowing a constant magnification system:

This has applications in photogrammetry – the use of photographs to determine the size and shape of objects, and in optical inspection systems.

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