Here comes a final remark - hopefully not too off-topic! I just want to mention the probably most basic and shortest way to determine the MTF:

Thorlabs adjustable LensMount

Canned Air (Dust-Off) Canned Air Dusters by Falcon Dust-Off. Available in refill cans also. See below.

Thorlabs KinematicMount

But my remark here is basically about processing the test image you sent, and the main thing is a hopefully more robust function for finding the star centers:

by SL Watkins · 2023 · Cited by 9 — The resulting exclusion analysis provides the most stringent limits in DM-nucleon scattering cross section (comparing to contemporary searches) ...

Thorlabs MirrorMount

I understand you have an image (as bitmap). This is an ( n, m ) array of bytes, and as first step you want to find those regions which show siemens stars?

Wow Henrik, I am impressed, although I am yet to start using your inspirational suggestions :-). Do you mind writing me a direct e-mail to vlado@vidilabs.com so I can give you some other material for you to look at which would be difficult to include here as attachment. But only if you have time and willing to continue with your suggestions :-)

Buy ProLights Eclipse-FS 36 Degree Lens Tube w/HQ Glass Optics online at BarnDoor Lighting Outfitters. 36 Degree optics for ECLIPSEFS profiler.

and than you can do things like siemensStars["BottomRight", "Center"] or siemensStars // Dataset. And you can convince yourself about the correctness of the above calculation like so:

Siskiyouopticalmounts

A test chart has 5 Siemens stars, one larger one in the centre and four smaller in each corner. [...] I have attached a real camera export ...

Ok Hans, this is what i would summarise it as: 1. A test chart has 5 Siemens stars, one larger one in the centre and four smaller in each corner. An image is taken by a camera and exported as JPG or BMP. How would you find the five circles and their centres? 2. Once the circles are found and their respective centres, one needs to measure the Depth of Modulation, as per the image I attached previously. Basically find how close to the centre the B/W rays are distinguishable with 10% contrast. 3. Based on the measurement under 2 (In pixels) calculate the MTF expressed in Line Pairs per Picture height. This is admittedly very easy if 1 and 2 are automated. I have attached a real camera export, which means they could always be slight variations in star positions, their geometry could be distorted (not always perfect circles) and have different resolution (which is to be measured).

Edmund Optics

Hi Wolframians, I am new to the Wolfram language, and I only used a trial version of the Mathematica to see if there is a way to replace my Siemens sine-wave star measurement for my test chart, using MatLab. I am under impression that Mathematica is much more powerful, but as with anything new, it is hard for me to find a function or algorithm of how I can measure resolution of a Siemens sine-wave star, which I use in my ViDi Labs test charts (https://vidilabs.com/testcharts.html) and developed a little program using MatLab to find the circles in an image, and then measure resolution (or MTF = Modulation Transfer Function), based on the 10% Depth of Modulation, as described by the IEC 62676-5 standards. If anybody can help me in either giving me a list of functions to look at, or perhaps somebody would know exactly how to calculate the above mentioned resolution, I would gladly purchase a full licence of Mathematica and investigate this further. Happy to consider even paying somebody for their time if they can do what I have described in my video in the able mentioned URL link. I am also adding an attachment, a simple explanation on how this resolution is measured. Thank you so much.

by RT Constable · 1991 · Cited by 82 — Increased resolution allows for better detection of small, high contrast pathological features, but at some cost. Increasing resolution leads to a ...

The image of a "Delta peak" is the point spread function (PSF) - and its Fourier transform is the sought-after MTF. Making the realistic assumption of a rotational symmetric PSF, one can make use of the Fourier slice theorem: A projection of the 2D-PSF gives its Abel transform (1D), and the Fourier transform of the Abel transform gives the radial data of the (rotational symmetric) MTF:

Your impression is absolutely correct! Here comes an attempt showing some intermediate result which hopefully points to the right direction:

Opticaltable

OpticalMirror Mounts

UVPLASTIC™ Light Diffuser and non-glare light diffuser sheets are made of polycarbonate plastic, which is mainly used as the cover protection for downlights, ...

Jul 8, 2024 — The hole is so small that most pinhole cameras operate at f-stops around f128-f256. These incredibly small apertures mean that you need equally ...

Features:This test card is specially designed for testing polarized effect.Portable: Compact and lightweight, the test cards are easily portable, ...

Thank you Henrik, You certainly are one of a kind. Your suggestions are definitely putting my thoughts in the right direction. All I need to do now, study Mathematica myself and see how I can proceed from your suggestions. I am happy to even pay for your time if you wish to complete my test chart evaluation, of which the Siemens star is probably the most convoluted, if I may say. But, I leave this up to you, I know this is not the place to discuss such outcomes, but wanted to show you my appreciation. I appreciate you time Henrik and thank you again for the good pointers and examples.

Here is a first attempt to find a (simple) circular structure in an image. First make the image. Define its limits and what else is needed

STANZ (Tm) Magnifier Clamp Lamp Magnifying 60 Leds Light 5" Lens 5 Diopter for Workbench. SKU: 10560460.

Thank you Hans, thank You Henrik, The last response from Henrik seems to be what I am after, and it is very promising. I am not sure why you didn't see the original image I had attached in my last response, as I used the "Add file to the post". But I am now attaching the original real export of a CCTV camera (typically they are HD or 4k resolution) and the measurements that I have made using Matlab. As you can see I am also measuring other parameters of the reproduced test chart, like the colour, Gamma and noise. I am not very happy with the Siemens star measurements, as they are not consistent with what I measure manually using PhotoShop for example. This is the reason I intend to try Mathematica, which I have no experience with, but willing it to try. I am assuming, finding the colour coordinates of the colour patches would be easy, and so would the random pixel noise of a grey patch representing 50% grey. Thank you very much for this hint Henrik, I will try and reproduce it myself on the real test chart and calculate the Depth of Modulation.

Optical mountfor lens

Laserline Optics Powell Lens Store. Fan Angle Choose an option 1 degree 5 degrees 10 degrees 20 degrees 30 degrees 45 degrees 60 degrees 75 degrees 90 degrees.

Seemingly mild businessman Edmond Burke (William H. Macy) visits a fortune-teller and hears a remark that spurs him to leave his wife abruptly and seek what ...

Hi Vlado, sorry for the delay! Here is a sketch of my approach for finally calculating the MTF (according to the formula you gave). I am assuming we have defined the above siemensStars association, then: