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I am not sure how to ask this question. Hopefully, I will edit it to make better sense as we go.

I have an image with 10 μm wide black and white stripes and I project it onto the imager, with 1000 pixels, 10 μm square each. Do I have to do image magnification in order to achieve 10 μm resolution. That is, being able to resolve black and white stripes?

My speculation:

I fill like if the line centers will be 'in phase' with the pixel centers, I will be able to resolve them. However, if the line centers will fall between the pixels, each line will take up two pixels, meaning that I will not resolve them.

I can not change the size of the pixels, but I can change the magnification of the image/stripes. Do I follow the Nyquist principle? In this case, if I understand right, the lines should be at least twice wider than the pixel's width. So, to make it happen, I must magnify the image 2x. Do I understand it right?

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  • \$\begingroup\$ Not sure if I answer your question, so I put this as comment instead of answer. I believe your refers to microscope or camera. Let work on just the x direction. In your case, width of the sensor chip is 1000 pixels X 10 μm = 10,000 μm. For '1X' magnification, a line of 10,000 μm appears as left most and right most of the sensed image. If you change the lens focal length so that a line of 5,000 μm occupy full left and right of the sensed image, you have 2X magnification. \$\endgroup\$
    – EEd
    Aug 5, 2014 at 22:45
  • \$\begingroup\$ For camera (microscope same principle), bottom right change 200 to 300mm lens is 'relative' 2X magnification. google.com/… \$\endgroup\$
    – EEd
    Aug 5, 2014 at 22:48
  • \$\begingroup\$ In your case, you achieves 10 μm resolution on the 'image plane' by changing lens focal and lens-to-camera distance (named extension tube) so that a line of 10,000 μm appears as left most and right most of the sensed image. see camera illustration, microscope is same i00.i.aliimg.com/wsphoto/v0/1003532224/… \$\endgroup\$
    – EEd
    Aug 5, 2014 at 22:53
  • \$\begingroup\$ @Naz - Just to clarify, when you say "achieve 10 μm resolution" what do you mean? For example, do you need to resolve an image with black and white lines 10μm wide into black and white stripes, or do you need to resolve a small number of black to white transitions to within 10μm, and without subsequent image/signal processing? (I am trying to keep my comment simple, sorry if its got too simple) \$\endgroup\$
    – gbulmer
    Aug 6, 2014 at 2:07
  • \$\begingroup\$ Resolution at what modulation depth? \$\endgroup\$
    – GR Tech
    Aug 6, 2014 at 5:00

1 Answer 1

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Essentially yes, you do have a very broad understanding. But a couple of notes: Nyquist needs a little more than 2X, so call it 2X + or perhaps 2.1X or 2.2X. However, you still will see large moire fringes (aliased patterns between the pitch of the object to the pitch in the image plane).

How do you get the right lens? Well, magnification will be dependant upon Object distance, Image distance and the focal length of the lens.

You say that you "... have an image with 10 μm wide black and white stripes ..." which I assume means that you already have a lens in front of your imager, so what is needed in this case is that the magnification has to increase by 2X. It is likely that you are dealing with a optical system that has de-magnification (objects are likely to be larger than 10 um - magnification is less than 1). But the 2X (or 2.2X) can be applied. In general this means that you will change the focal length of your lense.

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  • \$\begingroup\$ Right, the object has 10um stripes on it, so image of that object, projected onto the imager, must be 2x+ in order to resolve the stripes (given the size of the pixel is 10um). Right? So, if my pixel size was 5um, I could have 1x+ magnification of the object to resolve the lines? \$\endgroup\$
    – Nazar
    Aug 6, 2014 at 15:06
  • \$\begingroup\$ "So, if my pixel size was 5um, I could have 1x+ magnification of the object to resolve the lines?" - lets just say that if your pixels were LESS than 5um you wouldn't have to change the focal length or object image positions. You use of 1X and 2X can be confusing, perhaps you should say additional magnification. In this case the additional magnification is 1X. But be aware that not all lenses can resolve a 4.6 um blur spot. \$\endgroup\$ Aug 6, 2014 at 16:13

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