Sinnott Mirror Real Profile
Introduction
The usual method of reducing the data from amateur tests, e.g., the Foucault test, is to find the errors in the readings relative to the readings which would be obtained from a parabola of assumed focal length and then integrate these errors to find the mirror surface errors. It is more general to process the readings to obtain the surface profile directly without reference to a desired surface. In this way the surface errors relative to any desired surface can be determined, and it will be shown that for the parabola, the distance to the point of best focus can be computed rather than assumed.
Input Data
On the applet front panel you can change three mirror parameters: clear aperture, focal length and squared eccentricity. Additional settings are available by pressing the Settings button (blue collored). It allows you to enter up to three different series (KE measurements) and up to ten mirror’s zones per serie or setup the light source. If you have not nough data leave the fields blank. From the settings panel are available also two other buttons, Example and Clear; the first fill the series with stored in the applet source KE data; the second button clear all series data. The Close button will leave the settings panel and redraw the graphic with the new options.
Analysis
You can visualize your mirror profile simple by pressing the Profile button after any changes in the input parameters (mirror general parameters and KE data). Notice that the surface-error curve is zero at the mirror’s center and edge. This choice gives very nearly the best possible fit of any mirror surface to a paraboloid. Finally, the numeric results of an analysis tell you when to stop working on the mirror. There are three quantitative measures of mirror quality.
Strehl ratio > 0.8
Strehl ratio is the fraction of starlight that ends up in the central peak of the Airy disk. A perfect mirror will reflect about 85% of the light from a point source into the central diffraction peak. Any deviations from parabola will smear some part of this light throughout the surrounding rings, and therefore reduce the resolution of your mirror. Strehl ratio better than 0.8 is the most commonly used threshold for a satisfactory mirror.
RMS < 1/14
The "root of the mean of squares" is a measure of how close a parabola can be fit to the measured shape of the mirror's surface. This is the quantity that is minimized when finding the closest parabola. This measure is an improvement over the Raleigh criterion (which states that the deviations should not exceed a quarter of the wavelength of light used) in that it weighs the relative contribution of deviations from parabola by the area of the surface segment.
Peak-Valley < 1/4 wavelength
This is the original Raleigh criterion for an effectively perfect mirror. The problem with this measure is that it doesn't take into account exactly how much of a mirror's surface deviates by a quarter wave, so different mirrors that satisfy this criterion can produce images of a dramatically different quality. This number is given only as an additional sanity check.
The usual method of reducing the data from amateur tests, e.g., the Foucault test, is to find the errors in the readings relative to the readings which would be obtained from a parabola of assumed focal length and then integrate these errors to find the mirror surface errors. It is more general to process the readings to obtain the surface profile directly without reference to a desired surface. In this way the surface errors relative to any desired surface can be determined, and it will be shown that for the parabola, the distance to the point of best focus can be computed rather than assumed.
Input Data
On the applet front panel you can change three mirror parameters: clear aperture, focal length and squared eccentricity. Additional settings are available by pressing the Settings button (blue collored). It allows you to enter up to three different series (KE measurements) and up to ten mirror’s zones per serie or setup the light source. If you have not nough data leave the fields blank. From the settings panel are available also two other buttons, Example and Clear; the first fill the series with stored in the applet source KE data; the second button clear all series data. The Close button will leave the settings panel and redraw the graphic with the new options.
Analysis
You can visualize your mirror profile simple by pressing the Profile button after any changes in the input parameters (mirror general parameters and KE data). Notice that the surface-error curve is zero at the mirror’s center and edge. This choice gives very nearly the best possible fit of any mirror surface to a paraboloid. Finally, the numeric results of an analysis tell you when to stop working on the mirror. There are three quantitative measures of mirror quality.
Strehl ratio > 0.8
Strehl ratio is the fraction of starlight that ends up in the central peak of the Airy disk. A perfect mirror will reflect about 85% of the light from a point source into the central diffraction peak. Any deviations from parabola will smear some part of this light throughout the surrounding rings, and therefore reduce the resolution of your mirror. Strehl ratio better than 0.8 is the most commonly used threshold for a satisfactory mirror.
RMS < 1/14
The "root of the mean of squares" is a measure of how close a parabola can be fit to the measured shape of the mirror's surface. This is the quantity that is minimized when finding the closest parabola. This measure is an improvement over the Raleigh criterion (which states that the deviations should not exceed a quarter of the wavelength of light used) in that it weighs the relative contribution of deviations from parabola by the area of the surface segment.
Peak-Valley < 1/4 wavelength
This is the original Raleigh criterion for an effectively perfect mirror. The problem with this measure is that it doesn't take into account exactly how much of a mirror's surface deviates by a quarter wave, so different mirrors that satisfy this criterion can produce images of a dramatically different quality. This number is given only as an additional sanity check.
Bellow is listed the applet tag, that allows you to customize it by start, including initialising of the mirror
parameters (diameter, focal length, squared eccentricity), light source type and wavelength; auto or user defined
scaling; setup series and scale color, plot window background and applet title.
Applet Tag:
Applet Tag:
- param name = "Title" value = "Mirror Real Profile by Roger Sinnott"
- param name = "Mirror Diameter" value = "200.0"
- param name = "Mirror Focal Length" value = "1200.0"
- param name = "Mirror Eccentricity" value = "1.000"
- param name = "Plot Scale" value = "0.5"
- param name = "Wavelength" value = "555"
- param name = "Source Type Index" value = "1"
- param name = "Serie 1 Color Index" value = "1"
- param name = "Serie 2 Color Index" value = "9"
- param name = "Serie 3 Color Index" value = "4"
- param name = "Scale Color Index" value = "10"
- param name = "Background Color Index" value = "0"