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 Post subject: NA - R - DOF
PostPosted: Mon Oct 18, 2010 8:07 am 
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I bought myself a new camera last weekend and started wondering about what the 80% increase in pixels it has compared to my old one would do to my photomicroscopy.

The M400 has a NA of 0.055 - 0.230 with the 2x aux lens in place (the lower value being at the lowest magnification, the highest one at the highest magnification, right?).

So, in order to figure out it's maximum resolution I can do some simple math:

R=(0.61*wavelength)/NA (from here)

which, at the middle of the spectrum, and with full mag, would be (0.61*550)/0.230= 1458,70nm or 686 lines/mm

right? Now... my old Olympus E-510 has a pixel density of 4.1 MP/cm² which (in my head) implies that it can handle a resolution of 202.4 lines/mm... (√4100000=2024, so that's 2024pixels/cm, or 202.4 pixels/mm... I'm assuming that pixels can become lines, right?)

Am I on the right track here? (there is way more questions but let's check these basic assumptions first...)


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 Post subject: Re: NA - R - DOF
PostPosted: Mon Oct 18, 2010 9:49 pm 
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This post has been edited to use the corrected information Tim provided in his third post down on this page of this thread.


Tim wrote:
The M400 has a NA of 0.055 - 0.230 with the 2x aux lens in place (the lower value being at the lowest magnification, the highest one at the highest magnification, right?).

So, in order to figure out it's maximum resolution I can do some simple math:

R=(0.61*wavelength)/NA (from here)

which, at the middle of the spectrum, and with full mag, would be (0.61*550)/0.230= 1458,70nm ...

right?


Up to this point, right so far. Firstly let me say that is a remarkably good NA for that type of microscope.

Secondly, the resolution formula R=(0.61*wavelength)/NA is usually referred to as the Rayleigh equation.

And lastly, the following has too many numbers and too many multiplications and divisions to be of interest to anyone but the hard-core microscope imagist. Ah well, let's begin...

Your objective lens has a resolution of 1.46 um (where um = micrometers, a little bit easier unit to work with, compared to nanometers). Note that this is as close together two objects can get to each other and still appear individually in the image produced by the objective. If they are any closer together, they blur together in some diffraction-based jumble.

Now from the Olympus spec sheet you linked to, the CCD of your camera has area 17.3 x 13 mm and image size is (presumably) 3648 x 2736 pixels. Dividing 17.3 mm by 3648 pixels gives 0.00475 mm per pixel, or in more sensible units, 4.75 um per pixel. Dividing 13 mm by 2736 pixels also gives 4.75 um per pixel. Since the value is the same for both horizontal and vertical, the CCD has square pixels with length 4.75 um.

Now we know that the Wild has an objective magnification 3.2x, that becomes 6.4x with the 2x auxiliary lens. Multiplying the minimum distance that two objects can be resolved, 1.46 um, by the magnification, 6.4, gives about 10 um as the minimum spacing in the image that can be resolved.

This image is presumably placed directly on the CCD by the objective+auxiliary+tube lenses, or maybe there is some other non-magnifying optics that transport the image to the CCD. In that case, dividing the minimum image spacing 10 um by the pixel length 4.75 um gives a value of about 2 pixels across the minimum image spacing.

So, according to the Rayleigh resolution equation and my rule of thumb, you could average together 2 x 2 squares of pixels without sacrificing image resolution. Another way of looking at it... if you can see significant image variation in a 2 x 2 square of pixels, it is a diffraction artifact and not a real feature. Bottom line... averaging 2 x 2 blocks of pixels, you could reduce your image to 1824 x 1368 pixels and not lose any resolution.

Sorry to bear this bad news, but this is definitely a case where more pixels does nothing to improve the image produced by the camera. Even worse, the additional pixels can lead to diffraction artifacts that may be mistaken as real features.

As noted below, the 2x aux lens actually increases NA along with increasing magnification to 6.4x, which is a good thing.


Last edited by Brian on Thu Apr 28, 2011 1:53 pm, edited 1 time in total.

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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 2:55 am 
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Thanks Brian, now I can stick to my old Nikon D40X forever (or until it breaks). You just saved me a couple of bucks :)

Btw, send me a PM with your address (I lost it) there is a BIG photo waiting to leave across the pond...

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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 5:51 am 
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Great! That's a crystal clear bit of information Brian...

here's the wild's spec sheet:
Image

The image is indeed being projected through the objective (and aux lens) only... the 1.25x binocular tube magnification the sheet mentions at the bottom is something I don't really know to pinpoint in the scope, perhaps that Gene can tell us where that is happening (in the path the light takes when it's being directed at the camera port or somewhere in between the prism that directs the light towards the oculars and the oculars themselves...)

Since I've removed the original photoport and have replaced it with a tube without any glass in it the other specs have become obsolete...

Quote:
I suggest not using the 2x aux lens for photography.


Following that spec sheet, removing the 2x aux lens drops my maximum NA to 0.115, thus lowering my resolution to (0.61*550)/0.115 = 2917,39nm. (2.91um). Cutting that in half gives me 1.45 x 32 = 46.4um as the minimum spacing in the image that can be resolved which is hardly any better than the 50um I am getting with the 2x in place... right?

and you mention another thing that arouses curiosity:

Quote:
some additional optics that (heaven forbid) magnify the image before it gets to the camera CCD


just about all systems I know do have a projection eyepiece living just in front of the camera's chip. Why the 'heaven forbid'? What does such a lens do to be bad? I always thought it was preferable in terms of aberration correction...

Again, there is more to this, I want to talk about DOF as well as the title of this thread suggests but let's get the resolution part down first.

Thank you a great bunch again, Brian, where would we be without you... :)


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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 9:57 am 
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This post has been edited to use the corrected information Tim provided in his third post down on this page of this thread.

Tim, I didn't realize the 2x aux improved the NA. So yes, you draw the correct conclusion from your calcs... keep it in place or remove it, either way you are overpixellating along the length by a factor of 2 x 2.

Also, I did these calculations for my camera and microscope, which doesn't have any of that tubing stuff to get in the way of where I put the camera. So I am able to put the bare camera CCD, no lens at all, right at the point where the objective+tube lens first creates the real image. I've measured the size of that image in my microscope (your results may vary some, but not much), and it has about a 13 mm diameter.

It is true that other microscope-camera systems use some optics to transport the real image to the camera CCD. But if you have set up your system so that the microscope image just barely fills the vertical dimension of the CCD, then (since that dimension is 13 mm) the transported image is not magnified any further than the original image produced by the objective lens. You don't want the transport optics to magnify the image produced by the objective+aux+tube any further, because increased magnification just adds useless overpixellation at the cost of reducing the field of view.


Conny, great, glad this information could help you save some money. Checking the D40x specs, it looks as though its CCD is composed of square pixels with length 6 um. So using the Wild microscope, you are only overpixellated by a factor of 1.6 x 1.6. So the camera is a good match to the microscope.


Last edited by Brian on Thu Apr 28, 2011 1:57 pm, edited 1 time in total.

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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 1:06 pm 
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I've found out that the real image in the M400 is sitting at ~ 12cm above the prism that picks up the light from the zoom objective. Coincidentally I already had that small chipped Olympus which turned out to be the exact right size for that real image. The entire image is way bigger than the 13mm on the vertical but the area of interest is just that: 13mm.

This new camera (a Canon 550D/T2i which I solely bought cause it allows me to shoot awesome high def videos, i'm not letting any pixels go to waste, don't you worry :D ) has a bigger chip: 22.3 x 14.9 mm and more pixels in it: 1.8MP which works out to pixels being 4.30um big (or small for that matter)...

50um / 4.3um = 11.6 pixels across the minimum spacing... heh... it's getting worse... :D

Which leads me to my next question... I can adjust the image quality of that new camera and trim it down to 2592 by 1728 pixels (half the res). I assume that the camera will group every group of 4 pixels and treat it as one, right? So that would give me 8.62um big pixels... Still overpixeling by a factor of 5.8... hehe... there is no rescuing this, is there? :)

At least the software that comes with that canon rocks the planet and will make my photomicrography even more enjoyable: high res live view on my monitor to which I can perferm a digital zoom of 10x before even taking a pic... Another cool realisation is that it doesn't get better with newer microscopes

But onto the DOF...

That M400 is decked out with a diaphragm. In the past, before digital photography and stacking software, one could squeeze the aperture a bit, sacrificing resolution, in order to get some more DOF in their shots. I have been doing that as well but it appears I shouldn't... With the advent of stacking software it's better to keep the resolution at it's maximum shoot a few more shots and to let the software introduce the dof, right?


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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 2:41 pm 
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Tim wrote:
Which leads me to my next question... I can adjust the image quality of that new camera and trim it down to 2592 by 1728 pixels (half the res). I assume that the camera will group every group of 4 pixels and treat it as one, right? So that would give me 8.62um big pixels... Still overpixeling by a factor of 5.8... hehe... there is no rescuing this, is there? :)


Yes, trimming down the photo size to half res does as you suggest and is much preferable. With the correction you provided on the third page, that makes for a very good match to the objective... no overpixellation.


Last edited by Brian on Thu Apr 28, 2011 7:51 pm, edited 2 times in total.

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 Post subject: Re: NA - R - DOF
PostPosted: Tue Oct 19, 2010 3:00 pm 
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Tim wrote:
But onto the DOF...

That M400 is decked out with a diaphragm. In the past, before digital photography and stacking software, one could squeeze the aperture a bit, sacrificing resolution, in order to get some more DOF in their shots. I have been doing that as well but it appears I shouldn't... With the advent of stacking software it's better to keep the resolution at it's maximum shoot a few more shots and to let the software introduce the dof, right?


Indeed, squeezing the aperture reduces NA to increase depth of field. I have an iris aperture on my objective lens designed especially to reduce NA, but I've never had much reason to use it.

Depth of field is inversely proportional to the square of numeric aperture: DOF ~ 1 / NA2. If one knows depth of field for one numeric aperture, then one can use ratios to find depth of field for another numeric aperture... DOF / DOF' = (NA')2 / (NA)2. Solving for the depth of field you want... DOF = DOF' * (NA')2 / (NA)2.

I've been pulling particles in and out of focus of an objective lens with a high NA, very narrow depth of field for most of a decade. If you trust my experience, you can use my rough values... DOF' = 0.5 um for NA' = 1.4. So just especially for you, a relation to find depth of field: DOF = 0.5 um (1.4)2 / (NA)2.

For the NA = 0.230 this relation gives DOF = 19 um. So take images every 15 - 20 um and stack 'em and you should be good to go.


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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 1:54 am 
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Tim, are you shooting tethered using the EOS Utility program that came with the camera?


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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 3:09 am 
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I like to use the iris diaphragm on my M400, in combination with stacking. By doing that I can many times reduce the nuber of needed images for the stack. Sometimes I actually squeeze the light path a bit more than the (by Wild) recommended average setting to further increase the DOF. Exposure time is still within reasonable limits. The latest image I published here was taken with 2.5 sec exposure. Magnification is about 75x.

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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 5:50 am 
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Luke, yes I will be as soon as my m42 adapter will arrive. That software is awesome...

Conny, yep, I've always used the diaphragm but following this conversation I will try and stop using it. I want to attach a dial gauge to my scope and start taking shots every 10 um or so. Taking those extra shots isn't really all that time consuming. A handy addition too, a dial gauge that is, cause I can use it to perform the duChaulnes method as well and get a rough idea of OTL stones' RI.

Brian, thanks for the overpixellation warning, it's noted and understood. I'm pretty sure I've encountered many diffraction artifacts already, at the scope's limit's there have often been things showing up on images that weren't there using my eyes. It'll be hard to find a chip with 50um pixels on it though... And I wonder what happens to that value when I zoom out... lemmie calculate...

NA changes to 0.055 on lowest mag... (0.61*550)/0.055 = 6,1um. Lowest mag = ~12x so it gets even worse there...

I'll be getting my adapter ring somewhere next week I suppose and run some test shots when it gets here.


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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 2:54 pm 
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This post has been edited to use the corrected information Tim provided in his third post down on this page of this thread.

Tim wrote:
Brian, thanks for the overpixellation warning, it's noted and understood. I'm pretty sure I've encountered many diffraction artifacts already, at the scope's limit's there have often been things showing up on images that weren't there using my eyes.


That's a nice rule of thumb.

Tim wrote:
It'll be hard to find a chip with 50um pixels on it though...


With the new information, now we know all you need is a 5um pixel, rather than a 50um pixel. That is doable.

Anyways, what kind of dial gauge do you have in mind that will let you move in 10 um steps?

Can't wait to see the picture stacked from photos taken in 10 um steps. Hyper-realistic!


Last edited by Brian on Thu Apr 28, 2011 2:00 pm, edited 1 time in total.

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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 4:51 pm 
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This one.

I dunno if it's neccesary or that it will work properly but I might give it a shot... I'll await the results without first.

On using averaging software to make it all blend: that's exactly was the stacking software does... partially... I think... :D

We'll see... adapter is on it's way...


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 Post subject: Re: NA - R - DOF
PostPosted: Wed Oct 20, 2010 6:02 pm 
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Gauge looks interesting. Maybe along the way, you can calibrate the knobs on the Wild for moving up and down. Paint a little mark on the knob itself, and you could make a tick mark at each rotation point where your gauge says you've moved 20 um. Shame that wasn't done in the first place.

Methinks I should trademark that term "hyper-realistic photographs".


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 Post subject: Re: NA - R - DOF
PostPosted: Thu Oct 21, 2010 9:55 am 
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Heh I just realized I have a anlogue dial just like that one and it is divided into 10 um steps. Will try it as soon as I find a proper way of attaching it to the M400. 8)

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