# The Naked Scientists Forum

### Author Topic: Pin hole cameras  (Read 4937 times)

#### syhprum

• Neilep Level Member
• Posts: 3772
• Thanked: 16 times
##### Pin hole cameras
« on: 04/01/2007 11:04:13 »
Having a south facing flat and clear skies this morning I decided to experiment with various "F" numbers to observe the sun, the best resolution seemed to be about F1000 with a 4000mm throw but the resolution was too poor to reveal any Sun spots (about 2 Min's).
Does anyone know what the ultimate resolution that can be achieved by a pin hole camera

#### chris

• Neilep Level Member
• Posts: 5295
• Thanked: 61 times
• The Naked Scientist
##### Re: Pin hole cameras
« Reply #1 on: 04/01/2007 11:18:25 »
syhprum - please forgive my ignorance, but what are these F numbers?

#### Mjhavok

• Sr. Member
• Posts: 468
##### Re: Pin hole cameras
« Reply #2 on: 04/01/2007 12:05:11 »
When in doubt. Google or wikipedia will find it out.

http://en.wikipedia.org/wiki/F-number

In optics, the f-number (sometimes called focal ratio, f-ratio, or relative aperture[1]) of an optical system expresses the diameter of the entrance pupil in terms of the effective focal length of the lens. It is the quantitative measure of lens speed, an important concept in photography.

#### daveshorts

• Moderator
• Neilep Level Member
• Posts: 2583
• Physics, Experiments
##### Re: Pin hole cameras
« Reply #3 on: 04/01/2007 12:47:50 »
The obvious limit on the resolution of the camera is directly related to the F-number (N)

N = ƒ/d
where ƒ = focal length
d = diameter of the apperture

The limit in resolution caused by light going through the hole from two places and ending up in one pixel.

I think this is going to lead to a limit on the angular resolution θmin of about:
sin θmin = d/f = 1/N

One ultimate limit on the resolution is the rayleigh criterion.

sin θmin = 1.22 λ/d

where
θmin is the smallest angle it can resolve whatever the lens system
λ is the wavelength of the light you are using
d is the diameter of the aperture

This is coming from the fact that a hole will produce a diffraction pattern, the smaller the hole the wider the diffraction pattern. And if you do the calculus to find out when two diffraction patterns are indistinguishable it is 1.22λ/d

So the limit on sin θmin  is going to be 1/N or 1.22 λ/d which ever is larger

Although I would have thought that taking photos at anywhere near the diffraction limit is going to be very very slow.
« Last Edit: 04/01/2007 12:49:27 by daveshorts »

#### syhprum

• Neilep Level Member
• Posts: 3772
• Thanked: 16 times
##### Re: Pin hole cameras
« Reply #4 on: 04/01/2007 13:30:52 »
Thank you for your formalisation of the probable results of my experiments, your calculations predict that the resolution at the highest f number I tested (4000) should be 0.85 Min's as I am no where near the diffaction limit, my estimate was 2.0 Min's but I made no precise measurements.
The next time weather conditions are suitable I will try smaller apertures

#### lyner

• Guest
##### Re: Pin hole cameras
« Reply #5 on: 06/01/2007 15:42:36 »
there is a nice compromise in the design of a pinhole camera.
You want the hole to be big enough to reduce diffraction - but the resolution of the image (the effective pixel size or 'blurredness') is equal to the size of the hole. Also, you need a big enough hole to let in enough light.  The best design of pinhole viewer for looking at sunspots is a very long 'throw' between pinhole and screen. A few years ago my son and I saw a huge and perfectly formed image of the Sun on our front door (white painted) and the 'pinhole' was, in fact, the keyhole of the back bedroom. The Sun was in just the right position at the rear of the house and we could see two excellent sunspots. The sun's image was several cms across - the  image distance was , correspondingly, several metres away. (Probably a twice - a - year situation for the Sun to be in just that position.)
btw I once scrounged a 0.5dioptre lens from an optician and, fitted into a 2m length of drainpipe with a screen in the other end; it made a worthwhile improvement on a pinhole (with a useful f number without a blurred image). Excellent sunspots could be seen and the sun's image was, as you'd expect, a couple of cms in diameter. I guess the same thing could be achieved using a suitably chosen bit of (concave) reflective metal. But now we're into simple telescopes and where do you stop?

#### syhprum

• Neilep Level Member
• Posts: 3772
• Thanked: 16 times
##### Re: Pin hole cameras
« Reply #6 on: 06/01/2007 20:43:06 »
During the transit of Venus about three years ago I converted my bathroom to a 'camera obscura' and used a 50mm x12 telscope as a projector.
I was able to obtain a Sun disk on the screen 500 mm diameter with more than adequate resolution to observe and photograph the transit
Later that year I was able to visit the historic Sydney observatory and compare my pictures with what they took about 120 years ago
« Last Edit: 07/01/2007 12:52:11 by syhprum »

#### The Naked Scientists Forum

##### Re: Pin hole cameras
« Reply #6 on: 06/01/2007 20:43:06 »