Formula

[sam2010]

Hello all,

For a given camera and at a fixed distance, I need to know what is the maximum
object size I can capture with the camera, what is the best formula to use?

In reverse problem, I have 10x10cm object size and the camera should fixed at
50mm. What specifications the camera should have in order to be able to capture
such an object?

Can anyone help please?
Thanking you in advance

[Shadowman]

Hi Sam,

I don't know if a formula is the way to go because 1) you have to know the height of your subject (which can be estimated), 2) you have to know how far away you are from your subject, 2) you have to know how much of the image will actually be captured by the lens. I read that a 3 foot tall figure will fill the frame at 100 feet with a 500mm lens, will fill the frame at 25 feet with a 100mm lens. I haven't tested out the 500mm estimate but I have tested the 100mm estimate. How much of the image height will actually transfer to the final image, I haven't checked out yet. If you like math, grab a tape measure, a subject, your favorite lens and go at it.

[Donald]

Hello all,

For a given camera and at a fixed distance, I need to know what is the maximum
object size I can capture with the camera, what is the best formula to use?

In reverse problem, I have 10x10cm object size and the camera should fixed at
50mm. What specifications the camera should have in order to be able to capture
such an object?

Can anyone help please?

Can you explain why you need to know such information?

[Steaphany]

You'll find for formula for the angle of View here:

http://en.wikipedia.org/wiki/Angle_of_view

and with a bit of trigonometry and knowing the lens to subject distance you can get your answer

[sam2010]

Thank you for your replies.
I need the formula to set up a research laboratory experiment.
My subject is 10cm height and fixed at 50mm from the camera front.

In fact, I have calculated the angle of view which depends on distance and subject
dimensions but in my understanding the formula does not consider any specification
of the camera, how can I relate to that?

I used camera focal lenght f and distance to subject value to calculate the near and far depth of field but the formula I use doesn't not take into account subject height, so same question comes to my mind how can I relate camera capability to subject size?.

Given the camera I have today: 2MP, 3.7 effectif focal lenght, F2, I cannot get a full image of my subject, so I have to choose a different camera and some calculation
are necessary before. Oh, my research budget is limited so I cannot get those funcy
and expensive cameras -

[sam2010]

Any help please as how to choose my camera?

[JonathanC]

So lets see if I understand the question first of all.
The thing that you want to photograph is 100mm square.
The lens to target distance is fixed at 50mm.
You want to capture the whole 100mm X 100mm target on the camera sensor.
OK so far?

Now for the questions.
You have a 2MP camera, that bit is OK, I think.
3.7 effective focal length. 3.7 what? mm? What does "effective" mean in your context?
f/2, I'm assuming, which doesn't mean a whole lot, yet. Is that the maximum? Is it a fixed aperture lens?
Do you know the sensor size in your current camera? This relates directly to the size of what you can capture based on other information.
Do you have a specification or model number of your current camera? This would help a lot.
Does the target have two or three dimensions? I'm asking because if its an oscilloscope screen (for example) that you're capturing, depth of field is a small issue. If its a tank of fish, its a whole different issue.
Do you need to capture fleeting moments, or can you use long exposures?

[sam2010]

Hello,
Thanks for trying to help, I really appreciate it.
My target is 3 dimensions, 10x10x10cm maximum.

Aperture = 2 is the maximum and is fixed
Focal length = 3.7 mm
Camera sensor format = 6x4mm

When trying to capture my object with this camera and at a fixed distance of 50mm,
I cannot get an image of the all object. Two options:
Move the object: how much theorically?
Get a new camera: what features the camera should have?

Thanks a lot for your help once again

[JonathanC]

Well lets simplify the maths as a first guess.
If we assume that you can only use a square part of your sensor to capture the square target, you will have a 4mm section of your 4mm X 6mm sensor in use.
Next we can use a pinhole analogy for the camera to target distance. If we treat the lens as though it were a pinhole we imagine light travelling in straight lines from the target, through the pinhole and onto the sensor. Thus by simple mathematics we deduce that as the target is 25 times larger than the sensor, then the target has to be 25 times further from the pinhole (lens) than the sensor. As the focal length of the lens is 3.7mm, it follows that 25 X 3.7mm is the lens to target distance. This gives a lens to target distance of 92.5mm.
This is approximate only, as lenses behave like pinholes, until you have to focus them. The focusing moves the lens away from the sensor so the sensor to lens distance is equal to the focal length when focused at infinity, but moves away from the sensor as the focus range decreases. At double the lens focal length spacing (sensor to lens) the image on the sensor is the same size as the target.
For a target to lens distance of 100mm, the sensor to lens distance is 3.8422mm, and the 100mm square target is going to project onto a 3.84mm square section of the sensor.
As to the depth of field that you can expect, well you'll have to wait for the clever people around here to chip in.

[Dave Humphries]

As to the depth of field that you can expect, well you'll have to wait for the clever people around here to chip in.

Indeed (although Jonathan has done quite well so far!)

You still haven't told us what it is you are shooting, how it is, or can be, lit (flash or natural), whether it is moving, potentially ruling out multi-second exposures, etc.

However, my gut tells me I don't need to do the math to know that you're never going to get enough depth of field at those distances and a conventional camera and fixed f2 lens, so focus stacking is going to be necessary - IF it is possible with the subject and assuming the lens will focus that close.

If you're that close to something that is a 100mm cube, the front face is going to obscure the depth unless it is transparent, so maybe the above is irrelevant.

Why not draw a 100mm box on a bit of paper and take some phots of it to get a feel for how the theory relates to your reality.

And as to moving the camera, how will that be done?

It would really help if you could tell us what it is

My only guess as to your motive is;
a) it is something awful, or
b) you've been told to work it out for yourself and not get anyone else to do it for your, or you'll lose marks for what I assume is some kind of school or university project.