Confocal system - how to calculate depth of field

[mm355]

Hello everyone,

I'm new here. I hope someone can help me with my problem. I need to find DOF of the system shown in the picture below. This is infrared confocal system which works with broadband infrared source (3-8um wavelengths). The detector is high detectivity IR detector with the sensor size of 300 um x 300 um. The pinhole in the setup is 50 um in diameter.
I've read on microscopyu.com about DOF and I'm not sure how to apply this equation in my case. My particular questions are:
1. The NA in the equation - how should I calculate it for my setup? Which NA is it?
2. How to calculate this e?
3. Which magnification should I use? In my case I've got M=2 from the detector side and 1.31 from the IR source side.
4. Maybe there is another equation I could use which could be easier in my case?

Thanks for your help,
Matt

[Warthaug]

Almost all the information you need is on the lens of your microscope.

NA refers to the numerical aperture - basically, a measure of the amount of light a lens can collect. This should be printed on the side of your lens. If not, go to the lens manufacturers webpage and find your model - they will all list the NA on the lens's data sheet.

Magnification refers to the lens itself - i.e a 100X lens would have a magnification of 100.

Note: magnification and NA are often listed as mag/NA; for example, I have a 100X, NA1.25 lens; it is labeled 100/1.25 right on the lens body.

e is a little more complex - it is the resolution limit of your system. In some cases this will be due to the physical limitation of your lens. In other cases this limit will be due to the physical limitations of your camera. If the former, e will be L/(NA*2), where L is the wavelength you are imaging. If the later, it will be the width of a pixel on the output image (i.e. if one pixel covers a 10umX10u area, than this value will by 10um). Simply calculate both numbers, and use the larger one.

DOF, in this case, is an estimate. May factors can alter it - your sample, immersion media, scope alignment, etc.

Bryan

[mm355]

Hello Brain,

Thank you for that. In my setup I'm using a combination of lenses not a single microscope objective so I don't know the NA. My setup is not a microscope, I've designed it myself. My question is how should I calculate the NA for my system (for which lenses in my setup the NA should be calculated) to use it in the DOF equation?

Thanks,
Matt

[Warthaug]

I'm not 100% clear as to your setup. Do you mean you have multiple lenses you can choose from, multiple lenses arranged in series, or multiple lenses is parallel (i..e. a stereo setup)?

If the first or second choices, than NA is generally determined by the objective lens (i.e. the one closest to the sample). If the later, I have no clue as to how to determine NA. For that matter, if these are not conventional lenses, This link tells you how to calculate NA, although I'm not sure how to do it in the real world:
[Only registered users see links. ]

Your only option may be to manually determine the depth-of-field. Assuming you have a high-accuracy focus drive, you should be able to image a sub-resolution florescent particle (i.e. quantum dots), and determine your depth of field by moving the stage by set increments.

To do this, dilute the quantum dots (QDs) to 1:100,000 or so, and put on a slide. This should provide a field of monodispersed QDs, separated by several focal volumes (if many of the dots blur together, use a larger dilution. Focus on the plane of dots, and the adjust the focal plane up and down. You should be able to establish a range where you can observe a airy disk around each dot - once that disk is lost you are out of the focal plane.

Most commercial confocal ave a dept-of-field of 500-700nm using a 100X lens. Depending on the degree of magnification you have, I would predict your system would be 700nm or deeper - the longer wavelengths you are using, combined with what sounds like lower degrees of magnification, will produce a deeper depth-of-field.

Hope this helps.

Bryan

EDIT: just noticed your image, so ignore what I wrote at the very beginning. It looks like you've built your own objective lens - i.e.. your lens setup looks an awful lot like what you would see if you took apart a commercial microscope objective. In this case you would need to determine the NA of the lens train between the sample and the pinhole, as it is the combination of those lenses which will determine the NA. It is probably easiest to simply determine it experimentally, as described in the later half of my post.

[mm355]

Hello Bryan,

Sorry for a mistake in your name last time and for such a long silence. A lot of things are happening at the moment.

I measured the NA experimentally by mounting a pinhole just in front of the ZnSe lens (the lens which is the nearest to the sample). I measured the diameter of the light cone and calculated the NA from this equation:

NA = sin (tan-1[D/2f]),

where, D is the diameter of the light cone entering the lens and f is the focal length of the same lens. So

NA = sin (tan-1[20mm/2*38.1mm]) = 0.25

Could you tell me where did you take the e = L/(NA*2) from? Do you have any reference for that. I'm also trying to locate a good reference for DOF equation.

Thanks,
Matt

[Warthaug]

Originally Posted by mm355

I measured the NA experimentally by mounting a pinhole just in front of the ZnSe lens (the lens which is the nearest to the sample). I measured the diameter of the light cone and calculated the NA from this equation:

NA = sin (tan-1[D/2f]),

where, D is the diameter of the light cone entering the lens and f is the focal length of the same lens. So

NA = sin (tan-1[20mm/2*38.1mm]) = 0.25

Could you tell me where did you take the e = L/(NA*2) from? Do you have any reference for that. I'm also trying to locate a good reference for DOF equation.

The e = L/(NA*2) came from:
[Only registered users see links. ]

The same webpage has some formulas for DOF:
[Only registered users see links. ]

Bryan