Strehl meter

The Strehl ratio is a good measure of the performance of an AO system. It is defined as the ratio between the peak intensity of an image divided by the peak intensity of a diffraction-limited image with the same total flux.

Using the Strehl meter

The Strehl meter is currently located in the directory


To run it without starting an IDL session, type

> start_nirc2_strehl_vm

or you may start it in IDL using the command

> start_nirc2_strehl

The following widget should appear:

The first step is to enter the path where the data is located. Then the starting image number should be entered. For example, for image “n0250.fits”, enter 250. Then enter the number of consecutive images to be analyzed. This number should be greater than or equal to one. The Strehl ratio will be calculated from each image separately.

If there are any background files, enter the first image number and the number of such images. It is highly recommended that a background be provided to obtain accurate Strehls. If a background image is not provided, the program will estimate the background from a circular annulus of sky in the vicinity of the star.

If autofind is set to “ON” then the program will then automatically locate the star. If it is set to “OFF”, the user will be prompted to select the star. The output of the program is a Strehl estimate and the corresponding residual wave-front error obtained using the Maréchal approximation.

Finally, the photometry radius may be set or left at its default value of 1.0”. This is the circular aperture used to calculate the photometry of the star.

The Strehl widget can also be used with SHARC data as follows:

How the Strehl meter works

There are three major difficulties in calculating Strehls:

  1. The total flux needs to be found. This is especially difficult when the pixel size is small and there are a lot of pixels to sum the intensity over. The amount of noise in each measurement may be small, but the total noise is significant. As a consequence, the area over which the photometry is estimated is limited (in the case of this routine, to one arcsecond radius), thereby overestimating the Strehl. Large radii give less biased estimates, but the estimates are very noisy (less precise). 
  2. The peak intensity needs to be found using pixelated, not sampled, data. Only the intensity averaged over a pixel is known. There is a loss of information, which is especially significant when the image has a low Strehl.
  3. The diffraction-limited PSF needs to be determined. This is relatively easy for monochromatic PSFs, but for wideband filters, the PSF depends not only on the spectral response of the filter but also on the spectrum of the source.

The following describes the operation of the Strehl meter.

The data in the neighborhood of the center of the image is extracted. The total flux is calculated over a circular aperture with a radius of 1”.

The image intensity is subsequently over sampled by a factor of 8 using FFT interpolation. Then the maximum of the value of this over sampled data is found. The maximum value is then divided by the total intensity over the circular aperture. The diffraction-limited image is found by modeling the Keck telescope with the 36 segments and the central obscuration. More detailed modeling of the aperture, such as including the spiders or the gap between adjacent segments, has not been done. Using discrete Fourier transforms, the perfect PSF is calculated on a four times over sampled grid and then rebinned to the right sampling. In this way, sampling vs. binning issues are minimized.
Running the diffraction-limited image through the Strehl meter and setting the Strehl
to be unity yields the normalization factor needed to define the Strehl.

Accuracy of the Strehl meter

The code is completely insensitive to sub pixel shifts for Nyquist sampled data (this is why the Strehl meter was written in the first place). It works extremely well for
high Strehls when Nyquist sampled, as has been shown in the CfAO Strehl competition ( The meter underestimates the Strehls when the Strehl ratios are less than 0.2. A solution to this problem will be sought. The Strehl meter has been implemented for the medium and wide cameras but has not been extensively tested. The accuracy of the algorithm will suffer when the pixel scale increases.

References: A paper on measuring Strehl, titled “Is that really your Strehl ratio?”, appears in the Proceedings of the SPIE 5490, 504-515 (2004).

Obtaining the Strehl meter

All the required files are found in the directory /home/nirc2eng/idl/nirc2_strehl/, or can be downloaded directly here.
All the IDL *.pro files, tarred and gzipped.
The compiled IDL code as an IDL sav file.
To run these files, start an IDL session and then type:

> strehl_widget

If you don’t have IDL, you can download and install free of charge the IDL6 virtual machine from the RSI website.

Then you can run the strehl_widget.sav file:

e.g. in Unix, type idl –vm=`strehl_widget.sav’

Strehl meter for arbitrary telescopes/cameras

You can also obtain a Strehl meter to be used with any telescope and science camera here.

To use it, do the following:

Create an image of the pupil of the telescope. Alternatively, enter the Keck pupil filename: ‘keckpupil.fits’.

Set the parameters: the pixel scale of the pupil (in this case, 0.07 m), the plate scale of the camera (9.94 mas), and the wavelength (1580 nm).

Click on “Calculate perfect PSF”. This will take on the order of a minute to a few minutes, depending on the performance of the computer in use. You do not need to recalculate the perfect PSF again unless you change the pupil, plate scale or wavelength. A new image will be created with the perfect PSF. Next enter the image whose Strehl you want to find. If the image is not background subtracted, set “estimate background” to ON. If there is more than one star in the field, set \223autofind!\224 to OFF. Then click “GO!”.

For more information, please contact