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VCS - Virtual Couder Screen©

... test your telescope mirror quickly and precisely with an improved Foucault Test!

What is VCS?

  • VCS brings Foucault to your computer
  • VCS simplifies and improves retouching (e.g. parabolizing) telescopic mirrors.
  • VCS emulates Couder-like zone screens on a computer's display - no diffraction effects and no need to have a real screen any more!
  • VCS compares zones automatically! All you need is an adequately resolved real-time Foucault shadowgram available on your computer (e.g. using a webcam).
  • VCS evaluates measured data real-time

System Requirements & Downloads

The software is available in two versions:
  • Version 2.1.9 for old 32-bit operating systems
  • Version 2.2.0 for younger 32-bit operating systems and 64-bit operating systems

Please select the download for your current operating system from the table below:
Windows XP 32-bit
Download Version 2.1.9
tested on Windows XP Professional SP3 - 32-bit
Windows Vista 32-bitDownload Version 2.2.0tested on Windows Vista - 32-bit
Windows 7 - 64 bittested on Windows 7 Ultimate - 64 bit
Windows 8Please note: This software is not tested on Windows 8!
Windows 10tested on Windows 10 Home - 64 bit

.Net Framework
The software was developed under MS.Net Framework 3.5. Check your computer if this framework or a higher version is installed!
You can find MS.Net Framework downloads e.g. here:

Please Note:

  • It is recommeded to run Windows with an administrator account!
  • Take care that the screen resolution is set to Full-HD 1920 x 1080 pixel!
  • In case of problems please go to section Troubleshooting!

Installation and Updates

First Installation
Unpack the zip-file and move file Virtual Couder Screen.exe to a folder of your choice (empty folder is recommended).
Update Installation
Unpack the zip-file and replace the current file Virtual Couder Screen.exe with the new one.

How to Use VCS - Virtual Couder Screen
Step 1 - Environment
Mirror-positioning, adjustment and centering of knife edge as well as showing the shadowgram on a computer screen as usual.
Please Note:
Do not use a very low cam- resolution or a high jpg-compression rate (which can be set for some cams). High compression reduces information ad results in unwanted pixeling.

Step 2 - Basic Settings
Start VCS - Virtual Couder Screen. You have to accept the license agreement first.
Please Note:
=>   All subsequently outlined settings have to be defined only once, the tool keeps these data - not necessary to start from scratch every time.
=>   As long as your setttings are not consistent you get an according status message (window bottom)

Tab 'Mirror'

Define the mirror's various diameters here.
Please note, that it is the optical diameter, which defines the outer diameter of the screen's outer zone!
The Chamfer Diameter is important for screen calibration.
All diameters shall be measured as exactely as possible!

Evaluation Settings
The settings in groupbox 'Evaluation' have to be defined in case VCS shall perform an automatical evaluation of entered readings (longitudinal and transverse aberration, surface error profile etc.)

Radius of Curvature
The mirror's radius of curvature (ROC)

Coefficient of Deformation
This coefficient defines the mirror's DESIRED surface.

Possible Settings:

  • Parabolic ... -1 (the negative sign indicating that in this case marginal rays intersect farther from the mirror than axial rays in Foucault) 
  • Hyperbolic ... < -1
  • Elliptic ...> -1 and < 0 (figure is an ellipsoid of revolution about a major ellipse axis) 
  • Elliptic ... > 0 and < 1 (figure is an ellipsoid of revolution about a minor ellipse axis)
  • Spherical ... 0

aus Jean Texereau, "How to Make a Telescope", Second Edition, William Bell Inc., page 73
Light Source
Defines whether the light source is fixed or moves with the knifeedge.

The base unit you use for radii and diameters. Millimeters or inches are possible.

The wavelength of radiation used for calculating the theoretical diffraction spot radius (Rho).
Usually the value 560 nm, to which the eye is most sensitive, is used. This value must be given in namometers [nm]!

Step 3 - Centering and Calibrating the Screen

Tab 'Control':

Use slider 'Size' to vary the screen's size.
The 'Position'-buttons are for centering the couder screen exactely on top of the mirror's shadowgram.

Calibrating the Couder Screen
Check checkbox 'Calibrate'.
You will see a red circle representing the Chamfer Diameter as defined previously.
It is recommended to withdraw the knife edge completely, so that the mirror is brightly illuminated and the chamfer defines the the visible diameter!
Now correct size and position of the red circle until it exactely matches with the edge of the mirror's reflecting area. That's it!
It is recommend to check the couder screen's calibration from time to time (e.g. after each set of readings).

Important Note:
Always use functionality 'Calibrate' to calibrate the couder screen's exact size and position. The (red) Chamfer Diameter is the only diameter that may be used for matching with the mirror's reflecting area!!

Smooth Graphic
Smoothes edges and lines. Use this option carefully, it often just produces a pretty picture but does not increase the precision of measurements.

=>   It is informative to make a simple pin stick, where the pins (nails) mark the exact position of the mirror center as well as the outer zone's effective radius.
Position the pin stick in front of the mirror and switch on the effective radii (checkbox 'Effect. Radii'). The pin stick helps to verify the screen's calibration.

The screen can be positioned with display-pixel resolution. The better your cam's resolution is, the more accurate the virtual screen can be calibrated and the more exact are your zone readings.
An example:
If the mirror diameter is 350mm and the shadowgram on screen has a width of 500 pixel you get a resolution of about 350/500 = 0.7 mm/pixel.

Do not use high jpeg-compression rates (which can be set for some cams). High compression reduces information ad results in sub-pixeling.

=>   For executing Foucault it is not necessary to have the entire mirror on the display. It is a good idea to zoom in as far as possible so that the shadowgram fills almost the full width of the cam's field of view (top and bottom mirror areas are clipped then but this does not matter in this case).

Step 4 - Zones and Apertures

Tab 'Zones'

This tab offers a great variety of methods for dimensioning your preferred screen zones.
Zone radii are either calculated automatically according to the entered parameters or may be manually defined (see 'Manual Definition of Zone Radii')

Count Zones
Defines the number of zones you want to use.

Zone Radii
Select the method how to calculate the inner and outer zone radii here.
  • Equiareal Zones
     - Each zone is of equal area
     - A center area (so defined) is subtracted in advance
     - Inner zone has same area as all the others
     - This method is - for example - used by N.O. Carlin

  • Equiareal + Outer Width
     - Outer zone area is determined by value 'Outer Zone Width'
     - Subsequent zones are of same area as outer zone
     - Inner zone has NOT the same area but is the residual between adjacent zone and excluded center (so defined) This method is - for example - used by Texereau and Couder

Outer Zone Width
Defines the width of the outer zone. Only of interest in case 'Zone Radii' is 'Equiareal + Outer Width'.

Effect. Radii
Defines the method how to calculate the 'effective' zone radii (or, as N. O. Carlin calls them, 'corrected center radii').
  • Texereau ... arithmetic mean (See How to Make a Telescope, 2nd Edition, 2.31) In case the readings shall be evaluated using the VCS intrinsic functionalities it is recommeded to select this type of effective radii!
  • Couder ..... geometric mean
  • N. O. Carlin ..... special algorithm, see his website
  • Pin Stick ..... R(effective) = R(inner) + zone height * 0.707

Apert. Height
The height of screen's apertures. Values can be defined as invariable for all zones or as growing with zone index.
  • R(inner) ..... height is equal to the inner radius of current zone
  • 15 ..... height is 15% of screen radius
  • 15 increasing ..... height is 15% of screen radius for INNER zone, and increases for outer zones

Exclude Center [%]
The percents of area that shall be excluded in the mirror's center.
'Exclude Center' must not be set to '0' in case 'Apert. Height' is 'R(inner)'(this would result in height = 0 for inner zone)

Screen apertures can be pivoted; this may be usefull for quick testing for astigmatism but needs the knife edge or slit to be rotated accordingly!!
  • 0° ..... horizontal
  • 90° ..... vertical

Manual Definition of Zone Radii

Besides the various algorithms of automatical calculation of zones VCS offers a way to enter radii by hand.
  • 'Toggle 'Manual Entry Mode'': Toggles the zones grid between editable and readonly mode. 
  • 'Reset Grid': Clears the whole grid
  • 'Accept Grid Values': Press this button after all values have been entered in order to redraw the screen with the current radii.

  • Always have a look at the status line (at the window bottom). It displays short infos in case of inconsistencies!
  • Keep the grid in Manual Entry Mode as long as you want to use the manually entered values. Switching back to readonly mode will replace your entries by automatically calculated values!
  • All entered values as well as the grid's status (editable or read only) are kept and reloaded with next launch.

Step 5 - Carrying Out Readings

Use the checkboxes at the bottom to switch effective radii, zone radii and the couder screen on or off.
The Foucault Test is executed zone by zone as usual. With a single mouseclick you can move to the next zone.

The order how zones are switched can be defined here:

  • 1-n-n-1: Pressing button '=>' zone apertures are shown starting from zone 1 till zone n and back from zone n to zone 1
  • 1-n-1-n: Pressing button '=>' zone apertures are shown starting from zone 1 till zone n and then switch back to 1 again. In this case there is an additional button '<=' available which always shows the next inner zone.

A quick an reliable procedure to take the readings is described in chapter Screen Test Procedure

Tab 'Readings'
Enter your readings here.
Combobox 'Readings' is for definig the number of series of readings you want to perform.
As soon as the readings are complete average values are calculated automatically (row AVG).
Additionally the software calculates all necessary data to display longitudinal and transverse aberrations as well as a surface error profile (for details see chapter Data Evaluation)

All readings are kept and reloaded when the application is relaunched or if a configurationfile (*.vcs) is loaded.

Data Evaluation

As soon as all readings have been entered, VCS performs an automatical data evaluation.
It is important to mention that this evaluation is according to the algorithm used by Jean Texereau ('How to Make a Telescope, 2nd edition, chapters 2.38 - 2.41).
No doubt, this approach has its limits in terms of absolute accuracy, but - despite that - gives a good impression of the mirror's current quality and instantly tells the mirror maker where the surface needs further retouching.
To my mind these evaluations are sufficient for a great part of the parabolizing process. When finishing the suface, it is of course recommended to transfer the readings that have been retrieved so precisely with VCS to other evaluation programs that are specially designed for this purpose and thus deliver more detailed results (Strehl-value etc.). Figure XP or Andreas Reifke's Focault Test Analysis can be recommended.

To carry out the evaluations, VCS needs to know some further data about your mirror. Please define these in tab 'Mirror'!
Important results are listed numerically in the readings-grid. These are:

This is the arithmetic mean of the entered readings.

Delta p'
The distance between the axial intersection of rays from a specific zone and the axial intersection of the central mirror rays for the perfect figure.
Following formula is used:
Delta p' = -k(h^2/R + h^4/(2R^3)
where k is the coefficient of derformation, h the effective zone radius and R the mirror's radius of curvature.

AVG - C(or AVG*2 -C)
The averages of readings minus offset factor C (in case of moving light source this value is doubled before C is subtracted)

Trvs. Aberr. / Rho
Calculated transverse aberration divided by theoretical diffraction disk radius

Long. Aberr.
The longitudinal aberration

Offset Factor C
This is a constant that will equalize as much as possible the deviation in either direction from the perfect figure.
There are several ways to change this factor:
  • Performing an automatical optimization:
'Optimize TA'. This triggers an automatical optimization of factor C until the extrema of transverse aberrations (TA) are equal and opposite in sign. The procedure is very much comparable to the process of focusing at the finished instrument. The focus is moved to a position that delivers the best picture.
'Optimize StD'. Varies factor C until the surface StD (Standard Deviation) error is minimal. Optimizing the StD error is often helpfull to find a balanced surface profile that indicates where the mirror needs further correction.
  • Manual entry
Using the up/down buttons
  • 'By Zone' 
which sets C in a way that the longitudinal aberration is zero for the selected zone

Graphical Representation of Data

All evaluation results can be shown in form of graphics. These are of course updated real-time as soon as any parameters or data are changed!
Press Button 'Show Graphics' to open the 'VCS - Graphics' window.

Longitudinal Aberation

The distances between the two graphs represent the actual longitudinal aberrations.

Transverse Aberation

The graph shows the relative transverse aberration, i.e. transverse aberration divided by theoretical diffraction spot radius (Rho).
If the entire graph is inside the green boundary-lines at +/- 1.0 the mirror meets the Raileigh Criterion and the wavefront error is less than Lambda/4 PV. The displayed ratio Maximum is less than 100% then.
  • The closer the graph is to 0 (and the nearer ratio Maximum is to 0%) in all zones, the better is the mirror! 
  • Press 'Optimize TA' in tab 'Readings' to optimize the transverse aberration automatically!

Surface Error Profile

The graph represents the actual surface errror indicating the zones where the mirror needs further correction.

'Sf. StD (Standard Deviation) Error'
is measured on on surface (Sf). Double this value to get wavefront error. Please note, that this error only represents the currently measured mirror profile and NOT the entire mirror. Do not mix this up with RMS Errors delivered by interferometry!

To get the surface error profile as precisely as possible the following is recommended:

Note: The error figure depends on offset factor C. Increase or decrease C to get a well-balanced profile - e.g. optimize for minimal surface StD error.

=>   As you can see in this example, the mirror - measured in 12 zones - is quite good but needs further correction at the edge.


Pressing button 'Create Report' compiles a report containing the graphics and other important informations. This report is then available on clipbord and facultatively can be saved to a file.

Auto Compare

VCS provides several mechanisms that support the user with comparing the zonal brighnesses.
Both zonal apertures are scanned in short intervals (typically 25 times per second), the color information of each pixel is then converted to grayvalues and finally the frequency of grayvalues is shown as histograms - one histogram for each aperture.

The form of the histograms as well as their centroide's vertical distance allows a precise rating of zonal brightnesses.

=>   To use Auto Compare it is strongly recommended to set the computers color resolution to 'True Color' (32-bit)Do not use any kind of pin stick or other equipment positioned in front of the mirror that is visible in the zonal apertures. This would produce wrong measurements!

Launching Auto Compare

To launch Auto Compare just check the 'Auto Compare' checkbox in the Control Center's bottom row.

Anti Seeing

Anti Seeing is often helpfull to reduce the influence of turbulent air ("Seeing") when comparing the zones.
The histograms and other displayed values are then the moving average of past n samplings.
n = 1 ..... no moving average
n = 10 ..... displayed histogram and values are the average of past 10 measuring intervals

Here is a short video (please turn on sound!)

The interval of samplings [milliseconds]
An interval of 40 milliseconds yields a rate of 25 samplings per second. Find a value that is appropriate for you.

Setting Up Auto Compare

Auto Compare needs some few parameters to be defined:

Image Color Balance
Set this field according to the color saturation of the evaluated shadowgram. This determines the algorithm used to transform screen pixel colors to grayvalues.
The shadowgram can either be colored or grayscale. In case of colored images the color of each evaluated pixel has to be converted into a grayvalue by VCS. Unfortunately there is no 'only right' conversion algorithm, but this depends on the shadowgram's hue and saturation. The human eye is normally most sensitive in the green spectral range, less sensitive in red and least in the blue range. Therefore, when converting to gray, the three color channels red, green and blue have to be variously rated:

  • Balanced
Select this if the shadowgram is color-neutral or has a moderate color cast.
With this setting the conversion to grayvalues uses a formula that includes all three color channels.
  • GREEN Saturated
Select this, in case the shadowgram has an intensive green hue.
Solely the green color channel is evaluated then whereas red and blue channels are skipped.
  • BLUE / RED Saturated
Analogous as above

  • It is recommended not to use red-, green- or blue-saturated shadowgrams, but to reduce color saturation to a moderate amount.
  • Most cam-drivers allow to set the cam's color saturation parameters in a way that the the cam already delivers grayscale images. If possible this is strongly recommended! In this case any fine-tuning as mentioned above can be skipped. Setting 'Image Color Balance' is then irrelevant!

Measured Area
VCS offers two approaches for automatically comparing left and right zone:

  • Aperture

When selected, VCS works similarly as you do when comparing zones visually. It evaluates the overall zonal aperture (marked red) and calculates the histograms basing on all these pixels.
This method might be beneficial in case of bad seeing or if the shadowgram is impure or of low quality (e.g. optical or imaging errors)

  • Eff. Radius

In this case VCS selectively evaluates a thin line that exactely matches the zone's Effective Radius (again marked red).

This method has several advantages:
Up till now it was necessary to work with relatively wide zonal apertures, as the human eye fails when comparing extremely narrow zones (because of diffraction and other effects).
Unfortunately these wide zones show brightness-gradients, so that - in consequence - finding a fitting effective radius is essential. Over the time various formulas for calculating effective radii have been developed, though all of them are still approximations (see the formulas defined by Texerau, Couder, Carlin or others).
This is no longer a problem with VCS!

  • 'Auto Compare' internally works as if there were zones that are only one pixel wide. Such narrow "zones" cannot show brightness-gradients. 
  • Finding the suitable effective radius is no longer critical as the evaluated (compared) areas and the radius generally are one and the same!
  • The user can be sure, that the readings he gets at the measuring instrument strictly correspond to the effective radius - however this radius is defined. This way he can calculate the mirror's current curvature with significantly higher accuracy. 
  • Histograms normally are slimmer and thus their congruency can be determined more exactely.
  • Especially the outest and often the inner zone can be compared more precisely


a) Left/Right or Differential Histograms
Frequencies of brightness (resp. grayvalues) can be displayed as either a separate histogram for left and right screen aperture or as a single differential histogram. To get a differential histogram, the difference between left and right histogram is calculated and then plotted as absolute values.
The screenshots shown here both base on one and the same state of zonal apertures.
Use the option buttons at the bottom to toggle between the types of display.

How to Interprete Left/Right Histograms
According to the Foucault Test's theory both zonal apertures will be dimmed equally and simultaneously, when the knife edge is moved sideways towards the optical axis (OA) and in case it exactely hits the current zone's 'center of curvature (COC).
=> Zone apertures or effective radii (depends on setting 'Measured Area') that change their brightness equally and simultaneously will show histograms whose centeroids move up and down the vertical grayscale-axis exactely congruently.

In case 'Measure Area' = 'Aperture', asymmetrical or vertically stretched histograms often indicate that zones are too wide.
Apertures of optimal width produce histograms that are bell-shaped and ideally of equal amplitude left and right.
You can often avoid this by setting 'Measured Area' to 'Eff. Radius'

How to Interprete a Differential Histogram
For zones (effective radii respectively) of equal brightness left and right the differential histogram has the following characteristics:
  • no distinct peaks, especially no distinct double peaks
  • area of histogram is small (ideally = 0)

b) Histogram Centroid Distance Indicators
In both histograms you can see a red pointer line. This line always marks the centroid of the overall histogram.
The distance between these lines is diplayed as number and additionally as bar (at right margin)

c) Congruence Value
This is a classification number describing the congruence between left and right histogram.
  • 100% ... histograms are absolutely mirror symmetric
  • 0% ... histograms do not overlap at all

Raise Amplitude
Use this slider to raise or shrink the amplitudes.
Attention: Peak values may be clipped this way!

Screen Test Procedure

A suitable and quick method for taking a series of measurements is in accordance with the one described by Jean Texereau in 'How to Make a Telescope, 2nd edition':

Step 1) Before testing, let the mirror remain on its support for several hours. A uniform mirror temperature is important.

Step 2) Adjust the knife edge quite perpendicular to the optic axis.

Step 3) Carefully align the knife carriage rail parallel with the optic axis by noting that penetration of the knife into the beam is unchanged as the carriage moves towards or away from the mirror.
To do this, start with the knife edge at the center of curvature for the small central area and move it laterally towards the optic axis until you get the shadowgram clearly visible. Now move the knife edge back longitudinally until the crest of the doughnut has reached the mirror's edge. Here again the shadowgramm has to be clearly visible. If not, adjust the testing apparatus until the doughnut's crest can be well seen when moving across the entire mirror.
Now secure the Foucault apparatus firmly to the support.

Step 4) Before toggling the couder screen to visible, take care that the mirror is uniformly illuminated (the knife beeing completely out of the beam), also the cam's parameters should be set in a way that the image is not overexposed (reduce Iris or dim the LED).
Now start, for instance, with zone 1. Move the knife edge along the optic axis until you find the position where both sides darken uniformly (distance between red pointer lines = 0) when the knife enters the beam.
Take a reading for this zone and write the value to the corresponding cell in the readings grid.

Step 5) Switch to zone 2. To locate this zone's center of curvature draw the knife longitudinally until the distance between the histograms is zero again (no lateral movement necessary!). Take a reading.

Step 6) Repeat step five for all other zones.

Optimal Lateral KE-Position
Is there an optimal lateral position of the knife edge when making the measurements?
Yes, tests have shown that the lateral knife edge position is optimal when the histograms are vertically situated in a range that is defined by the green lines as shown in the picture.

Utilities - Toolbar

The toolbar offers some convenient utilities. These are (top down):
  • Help button to launch online help
  • 'Load Configuration' for reading in a configuration file
  • 'Save Configuration' for writing the current software status (all settings, radii and readings) to a configuration file.
  • Make a screenshot and save it to a jpg-file

Registering the Software

VCS - Virtual Couder Screen© is shareware. Within a trial periode you can use all functionalities without any restriction. Please register the pruduct in order to use the software after the trial period has expired.

Version History

Version 2.2.0
    • fixed problems when running the application on Win 8 and Win 10 platforms

Version 2.1.9
    • added message to inform the user about the algorithm of evaluation according to Texereau

Version 2.1.8
    • minor change

Version 2.1.7
• redirected URLs to new VCS website

Version 2.1.4 & 2.1.5 & 2.1.6
• Made dependency  between moving o fixed light source and calculation of transverse aberration better visible
• Improved user guidance

Versions 2.1.2 & 2.1.3
• Added calculation and automatic optimization for minimal Surface RMS Error
• Fixed bug causing wrong absolute values of surface error profile and wrong display of transverse aberration / diffraction disc radius

Version 2.1.1
• Added recommendation for getting best surface error profiles

Version 2.1.0
• Automatic evaluation of measured data.
• Immediate calculation and graphical display of lateral aberration, transverse aberration, and surface error profile.
• Automatic optimization for 'best fit' transverse aberration
• Added Description of Screen Test Procedure
• fixed bug 'value zero not correctly restored from configuration file'
• set max count readings to 6

Version 2.0.5
• fixed bug 'statusmessages not displayed'

Version 2.0.4
• Auto Compare Mode (automatical brightness comparison of zonal apertures)
• Brightness evaluation across full aperture or exactely along effective radius
• 'Anti Seeing' mechanism
• Improved positioning and calibration of couder screen
• Improved definition of mirror diameters (outside-, chamfer-, optical diameter)
• Improved definition of zones and effective radii (according to Texereau, Couder, N. O. Carlin, Pinstick plus free definition of radii)
• Excludable screen center area
• Improved definition of 'Aperture Height'
• Pivotable screen orientation
• Software configuration can be saved as file or loaded from file
• Fixed bug 'Computer Screen Freezes'
• Improved software stability
• 'One click' screenshot to jpg-file utility
• Online Helpsystem
• Change of distribution type from freeware to shareware

Version 1.1
• Virtual screens and radii
• Effective Radii according to Texereau
• Variable zones count
• Readings management
• 'One-click' zones switching
© DI Hans-Heinrich Wenk - June 2022
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