**Presentation
of MTF Simulation of Lenses**

*Simulation of
the performance of photographical lenses*

The
software *MTF Simulation of Lenses* perform a simulation of the
performance of lenses. In fact, the user select any lens in a data
base and a picture. This picture is doe to the simulation modified as
the lens will do.

For the simulation the software compute and take in account the following parameters:

this curve indicate the -darkness of the picture on each point of the picture.*Relative -illuminance:*this curve indicate the distortion on each point of the picture.*The distortion:*the MTF graphs indicate the lost of precision on each point of the picture and for each spatial frequency (the measurement unit is the number of lines/mm).*The MTF (Modulation Transfer Function) graphs:*

There are 2 kind of MTF diagrams:

MTF tangential

MTF -sagittal

To process a picture, we need to work on a polar coordinates (P,I,J) on the concerned point (P) to process. O is the center of the lens, which is also the center of the negative film.

So OP is the image height (u on Zeiss data sheets). P' is the result of the simulation.

The distortion can be easily calculated with the formula:

P' is the new point resulted. The distortion is also a locally translation.

The principle of the calculation is to perform an FFT (in 2D) in the polar coordinates, perform an attenuation of the coefficients and perform the inverse FFT.

This FFT produce:

For the frequency 0, the illumination of the point P (called )

The tangential spectrum (every frequencies which can be in the form )

The sagittal spectrum (every frequencies which can be in the form )

So we obtain after processing the FFT the following result:

The
computation of the MTF and the relative illuminance consist of
multiplicating each A_{i,j} term through the coefficient of
attenuation M_{i,j} described later:

The
attenuation coefficient M_{i,j }
are:

M

_{0,0}: relative illumination on the point PM

_{0,p}: MTF sagittal on the point P for the frequency divide through M_{0,0.}M

_{k,0}: MTF tangential on the point P for the frequency divide through M_{0,0.}M

_{k¹0,p¹0}:

To perform the computation, Optical do first the translation caused by the distortion, then apply the calculation of the MTF and the relative illuminance effect.

When
*MTF Simulation of Lenses* is started the following main window
will be displayed:

Click
on *File->Open* to load a
data base of lenses. A demonstration data base (*demo.ldb*) is
delivered. It contain some data of fictive lenses:

*50mm:*a fictive lens*filtre_5_raies:*a lens which have a MTF equal to 0 on each point for a frequency of 5 lines/mm*filtre_10_raies:*a lens which have a MTF equal to 0 on each point for a frequency of 10 lines/mm*transparant:*a perfect lens which have a MTF equal to 1 on each point of the picture and for every frequency*filtre_sagital:*a lens which have all MTF -sagital equal to 0 on each point and for every frequency*filtre_tangentiel:*a lens which have all MTF tangential equal to 0 on each point and for every frequency

Click on *Data Base->Visualization* to see the characteristic
of each lens in the data base:

The first line contain the key for choosing the lens:

The manufacturer (here test)

The designation of the lens (here 50 mm)

The aperture (here f1.4)

The source of the measurement (here Photodo)

The -focale (here 50 mm, only as information)

To
start the simulation click onto *Operation->Simulation*
on the main window. The following window appear:

First choose a lens and then a source picture on which the computation will be performed:

*File:*the source a picture (gif, jpeg, xbm or bmp)*Sinus:*the source is a set of line with a frequency of x lines/mm and with an angle of y degree*Circle:*the source is a set of circles with x lines/mm centered on the middle point of the lens.

After it, select the output window. This window correspond to the size of the negative.

** Attention:**
Depending on the precision and the size of the window, the quantity
of the memory request and the computation time can be very important.
(for a whole 32mm negative with a precision of 40 lines/mm, the
computation can take a half day for a Pentiun 4)

The
last operation is the selection of the precision. It is possible to
modify it directly (using the text entry) or using the slider. If the
distortion should be calculated the field *distortion*
must be selected.

Now,
click on *simulate* to start the simulation.

After the computation, the result appear on a new window which permit to compare the simulated picture with the source picture:

It is possible to zoom in/out the simulated and the original picture by selecting an area with the mouse.

This is the result of the simulation of a lens with a distortion which go from +100% to -100%.

This example is the simulation of a lens which have a MTF equal to 0 for 5 lines/mm. The source picture is composed from lines with a frequency of 5 lines/mm. The result is a picture grey.

This example is the simulation of a lens which have a MTF sagital equal to 0 for 5 lines/mm. The source picture is composed from lines with a frequency of 5 lines/mm. The lens filter all lines which are going through the center of the lens.

This example is the simulation of a lens which have a MTF tangential equal to 0 for 5 lines/mm. The source picture is composed from lines with a frequency of 5 lines/mm. The lens filter all lines which are tangential to a circle centered on the center of the lens.

When the source picture contain only some circles with a spatial frequency of 5 lines/mm , the result is a picture fully gray.

Author*:* Sebastien Fricker

*E-Mail:* friseb123@users.sourceforge.net