A Little Help with Equations

[HenryChavez]

I came upon a couple of equations and decided to use them on a proven pinhole camera I own. This camera takes really "sharp" images for a pinhole camera. I always guessed that I was getting these good images as a result of hitting the sweet spot, the Airy disk. The camera is a 4x5 made from a cigar box. These are the specifications:

Camera: 4x5
f/250
Focal Length = 90mm
Pinhole = Laser made and purchased
Pinhole Diameter Size = .350mm
Pinhole Material Thickness = .025 (actual specs are .019 - .050)

I'll post a photo sample if anyone is interested, but I am more interested in the following equations that were obtained from an article titled, THE COMPREHENSIVE TECH GUIDE TO PINHOLE PHOTOGRAPHY, postedMarch 6, 2013 by Udi Tirosh. Mr. Tirosh, if you are here, thank you for your post.

view angle = tan^-1( (d/2)/(t/2) ) x 2 {my solution was 172}
image diameter (mm) = 2 x focal length x tan ((View angle)/2) {my solution was 2502}

Actually, the second equation interested me most. That said, I needed the first to come up with the second. When I obtained the result for the "image diameter" and compared it to the film diagonal (163) for my 4x5, I was struck by the difference in size. This made sense as the centermost portion of the light was what was captured, the Airy disk. Now, just so everyone understands. I am not making a point and calling this fact. Far from it. I am asking, is this correct? Am I missing something?

One last thing. I am a math dingus and often times I am really out of my depth. In my later years I have grown to like math and wish I had listened in school. I like this sort of math, but as I said, out of my depth.

Best,
Henry

[HenryChavez]

I found an error. The tangent calculation is wrong because of type.

[MartinS]

Hi Henricus,

interestingly, your camera exactly matches the Prober-Wellman optimum for sharp pinhole image, at least for 560 nm wavelength (roughly green light) and landscape, or non-macro, photography. The theory can be found here, a convenient calculator based on their equation is here.

Best regards,
Martin

[HenryChavez]

Hi Henricus,

interestingly, your camera exactly matches the Prober-Wellman optimum for sharp pinhole image, at least for 560 nm wavelength (roughly green light) and landscape, or non-macro, photography. The theory can be found here, a convenient calculator based on their equation is here.

Best regards,
Martin

Thanks for the response. I'm familiar with the PW white paper. I wish I could say that this camera was a result of reading it. Truth be told, the camera was conceived around a cigar box. I had a cigar box that had a sliding lid and my film holder perfectly fit the slot created by the sliding lid. Once I decided to make a pinhole with it, I used calculations found here to choose the pinhole size based on the size of the box. I was amazed at the sharpness of this camera and has been my favorite ever since. As a matter of fact, we recently had a massive flood here in Houston and this camera was damaged as a result. I am almost finished fixing it. I had to replace the leather and some of the brass furniture. I'm waiting on a replacement ghost levels. I can't wait to use it again.


Our Lady of Lourdes Catholic Church by Henry Chavez, on Flickr
4x5 Pinhole by Henry Chavez, on Flickr

[MartinS]

Really nice camera, and the image is perfect. Good luck with the camera (and possibly home) repair.