DIY 4x5 Pinhole Math...

ChristopherCoy · May 1, 2021

I have about six 4x5 film holders, and I've been having the itch to try LF again. Combine that with the recent discussion of WPPD, and, well.... this is where I've arrived. I want to build my own pinhole camera and utilize the 4x5 holders I already have.

I've located an eBay seller that sells laser drilled pinholes anywhere from 0.1mm to 1.0mm. I figure $10 for a precision drilled aperture, and some scrap wood I have in storage isn't such a bad investment. The problem is that I have to math. I hate to math. I've never been good at math-ing.

I've found some instructions online and this is where I am:

Pinhole diameter: 1.0mm
Pinhole thickness: .05mm
Focal length: (1.0mm / 0.03679)2 = 738.82mm

That focal length equates to a roughly 29" long box. I've tried to figure out the angle of view using view angle = tan-1( (d/2)/(t/2) ) x 2, and I think I'm getting about 62°.

And at this point, I'm not even trying to figure out the image diameter projected at a 29 inch focal length.

So, where am I going wrong and how do I get this down to more reasonable dimensions while still ensuring that I have the best image at the film position?

BrianShaw · May 1, 2021

Consider the smaller pinholes. Consider closer to “normal focal length equivalent “. Download Eric Renner’s pinhole book if you haven’t already. Look up “Black Cat extended exposure calculator”... not necessary but nice.

ChristopherCoy · May 1, 2021

OK, so .6mm gives me 266mm or a roughly 10.4" box. But that also gives me a 37° angle of view.... correct?

Does that give me an image diameter big enough to cover the 4x5 film?

ciniframe · May 1, 2021

I believe you are overthinking this. Just look at the spec on a 4x5 pinhole you can buy and then use those as a guide. For instance;
The Harman Titan 4x5 pinhole camera uses a .35mm hole for a 72mm focal length, or f206
(the distance from the hole to the film),
72mm is about a standard wide angle for 4x5, about equal to a 22mm lens on a 35mm camera. (Direct comparison between 4x5 and 35mm full frame only approximate due to different aspect ratios).
You didn’t state what angle of view you wanted but samples from this camera shows that it covers 4x5.
There is a Harman Titan group over at Flickr if you wanted to see results from that combo.

radiant · May 1, 2021

Why don't you use calculator?

https://www.mrpinhole.com/calcpinh.php

4x5" needs 81.3mm image circle radius (162 diameter).

You need to use 0.389mm pinhole with 68.9mm focal length to cover 4x5".

ChristopherCoy · May 1, 2021

vedostuu said:
Why don't you use calculator?

https://www.mrpinhole.com/calcpinh.php

4x5" needs 81.3mm image circle radius (162 diameter).

You need to use 0.389mm pinhole with 68.9mm focal length to cover 4x5".

According to that calculator, that focal length only gives me a 132mm image diameter, which means vignetting on the corners.

ChristopherCoy · May 1, 2021

Although the "design wizard" seems to simplfy it to a single mouse click.

radiant · May 1, 2021

ChristopherCoy said:
According to that calculator, that focal length only gives me a 132mm image diameter, which means vignetting on the corners.

You are right. That calculator isn't error-free it seems.. But glad that wizard helped you finding correct values!

radiant · May 1, 2021

I think the wizard is giving some strange solutions.. You don't need 299mm coverage for 4x5" ?

I re-calculated that 85mm / 0.389mm should give 163mm coverage and be enough for 4x5" .. Harman Titan's 72mm focal length is too shallow for 4x5"?

ChristopherCoy · May 1, 2021

vedostuu said:
I think the wizard is giving some strange solutions.. You don't need 299mm coverage for 4x5" ?

Just to check things, I did it backwards. I googled (since I don't shoot LF) "normal focal length for large format" and used the result of 150mm. Then I went to the camera design wizard and chose "focal length", entered the 150mm and then the film dimensions of 4x5". It's still coming up with 288mm of coverage.

Donald Qualls · May 1, 2021

I get good results at "normal" focal length of about 135mm with a 0.5mm pinhole (= f/270) in my 9x12 cm plate cameras. This is close enough to 4x5...

A pinhole generally has HUGE coverage. I have one camera with the pinhole in the end of an old RA-4 paper roll core, and it covers from about a half inch behind the hole, all the way around. Coverage limitations are more to do with light fall-off due to the increasing distance from pinhole to film/paper as the angle gets wider than anything else. If you have a 60mm focal length on 4x5 film, the corners get around two stops less light than the center of the film. Go wider, to 30mm, and that becomes three stops. There comes a point where you run out of film latitude -- the center will be blocked up due to overexposure, while the corners are so underexposed you only see the brightest highlights.

MattKing · May 1, 2021

With pinhole design, you need to start first with your film size and what angle of view you wish to record.
If want the image to cover something like the 163mm diagonal of a 4"x5" sheet of film, you could do so with a short focal length to capture a wide angle of view, a medium focal length to capture a medium angle of view or a long focal length to capture a narrow angle of view. But there is a minimum focal length that it is impractical to go below, because of fall-off concerns. The first calculator linked to builds into itself an assumption about that.
So to use the first calculator in a situation where you get to pick the dimensions of your camera, fill in (in the left column) the film dimension of 163mm (the diagonal of the sheet) and then try a few different focal lengths, clicking on "Calculate" each time.
As you vary the focal length, each calculation will reveal (in the right column) two different Optimal numbers (Diameter of pinhole and Focal Length) as well as Image Diameter and Angle of View.
Initially, you will ignore the Optimal numbers, and pay attention instead to the calculated Image Diameter and Angle of View numbers, which are determined entirely by the focal length and the size of the film - the pinhole size has no affect on them.
If you want the image to go corner to corner, you need an Image Diameter number that is at least as large as the 163mm diagonal of the film, but it can be larger. If it is larger, the actual angle of view on the film will be narrower - you will be recording on film less than the full image.
After trying a few different focal lengths, most likely you will find that 85mm is the minimum length that will give you an Image Diameter of at least 163mm. Note however that that results in an almost 88 degree Angle of View, which is quite wide. If you want a narrower angle of view, try a few longer focal lengths (calculating each time) until you arrive at an Angle of View you like.
Now, once you have arrived at the focal length (and Angle of View) you want, it is time to make use of the results of the Optimal Diameter (of pinhole) calculation. Read that number from the left column, and enter that number into the Pinhole Diameter field in the right column. Calculate will then reveal the resulting f/stop and a match between the actual and optimum Pinhole Diameters and Focal lengths. Use those numbers to, respectively, order your pinhole, and build your box.

ChristopherCoy · May 1, 2021

hunh... focal length of 145mm with a pinhole of .5mm give's me a true F295.

MattKing · May 1, 2021

ChristopherCoy said:
hunh... focal length of 145mm with a pinhole of .5mm give's me a true F295.

View attachment 273465

Which is not quite optimal, according to the calculator.
Try .528 diameter and a focal length of 156 mm.

ChristopherCoy · May 1, 2021

MattKing said:
Which is not quite optimal, according to the calculator.
Try .528 diameter and a focal length of 156 mm.

I’ll check with the seller and see if they can get that accurate with the hole.

BrianShaw · May 1, 2021

ChristopherCoy said:
I’ll check with the seller and see if they can get that accurate with the hole.

When you ask, make sure you include your required/acceptable tolerances.

MattKing · May 1, 2021

ChristopherCoy said:
I’ll check with the seller and see if they can get that accurate with the hole.

I'm sure .53mm would be excellent, and .5mm would probably be fine.
It is a pinhole, after all.

DWThomas · May 1, 2021

Did one ten years ago (good grief it's been THAT long?!!! ) 4x5 Pinhole Mostly made from scraps around the workshop. Homemade 0.30 mm pinhole at 62 mm pinhole to film distance (fairly wide), approx f/210. It works quite well -- but then a few years later I incorporated some of the same design ideas at 8x10.

Mr Pinhole is good in that it runs in a browser. But there is an old and not recently updated Windoze program, Pinhole Designer, which is much more informative on what mumbo-jumbo assumptions it makes in its calculations. I consider Mr Pinhole to be a bit of a pessimist! And in truth, the pinhole equations seem to be fairly broad curves -- one can get pretty far off and still see half decent results. (Ref: "Don't overthink it!")

grahamp · May 2, 2021

I put a 0.3mm (approximate) pinhole on the front of a Will Travel 58/65mm 4x5 body for this year's WPPD. That's around 55mm actual pinhole to film, and around f180 (for ease of calculation from the light meter). There's just the beginnings of vignetting in the corners, possibly because the brass sheet I was using was a touch thick. But the results work for me.

ChristopherCoy · May 2, 2021

MattKing said:
I'm sure .53mm would be excellent, and .5mm would probably be fine.
It is a pinhole, after all.

He can't get down to .528mm accuracy. The closest he can come is .53mm using hand broaching tools.

I'm just going to go with the .5mm which is .002" thick. As you said... it is pinhole.

ChristopherCoy · May 2, 2021

DWThomas said:
Did one ten years ago (good grief it's been THAT long?!!! ) 4x5 Pinhole Mostly made from scraps around the workshop. Homemade 0.30 mm pinhole at 62 mm pinhole to film distance (fairly wide), approx f/210. It works quite well -- but then a few years later I incorporated some of the same design ideas at 8x10.

Mr Pinhole is good in that it runs in a browser. But there is an old and not recently updated Windoze program, Pinhole Designer, which is much more informative on what mumbo-jumbo assumptions it makes in its calculations. I consider Mr Pinhole to be a bit of a pessimist! And in truth, the pinhole equations seem to be fairly broad curves -- one can get pretty far off and still see half decent results. (Ref: "Don't overthink it!")

Nicely done! I wish I had the ability to figure out angles, and the tools to make cuts like these.

Donald Qualls · May 2, 2021

Worth remembering, too, that the wider your angle, the sharper your resulting print will be (final print sizes being equal). That is, a 60mm on 4x5 will need less enlargement and thus produce a sharper print than 60mm on 6x6, but it'll be comparable to 30 mm on 6x9.

ChristopherCoy said:
I wish I had the ability to figure out angles, and the tools to make cuts like these.

Something like that can be solved graphically (you know the front plate dimensions and the box size, which gives you the front and rear edges of the angle pieces; the others will come out of Pythagorean theorem, which is pretty basic math). Or just cut the angle pieces from scrap card stock, held together with tape for mocking up, and only transfer to wood once you have it fitting.

ChristopherCoy · May 2, 2021

Donald Qualls said:
...the others will come out of Pythagorean theorem, which is pretty basic math).

Have I ever mentioned that I graduated HS with a 2.1 GPA because I was taking art II, III, IV, and Advanced Photography all in the same year? My version of basic math is "if Johnny has three apples and drops one, how many does have?"

Donald Qualls · May 2, 2021

Got a smart phone? Download a calculator app (I use one that emulates an HP-41CX). Squares and square roots are all that's needed, but few non-scientific calculators make both easy.

Admittedly, I learned to do much of this stuff on a slide rule, before calculators were either common or affordable -- but really, Pythagorean formula for a right triangle is easy enough they teach it in fourth grade (or did when I was that age).

ChristopherCoy · May 2, 2021

Actually, I passed geometry with a 98. It was the only class that came naturally to me. I remember one time I was sleeping in class. I had my head down on my desk and I was apparently snoring. The teacher, Mrs. Vestal, came by and slammed her book on my desk. She said "if you can answer the question, you can go back to sleep." I lifted my head up, read the question on the projector, answered "123xyz", and put my head down without missing a beat. I remember her saying "how'd you know that?", and being shocked that I was able to answer correctly.

The problem is that I can't remember any of the basics. Bout the only thing I remember is a right triangle. Maybe I should brush up on it a little and see what I remember.

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