# Calculation of final magnification when using a CCD camera

I'm trying to empirically calculate the approx final magnification (mag) of digital images rendered through our confocal microscope. Using a micrometer and the microscopy equipment I have, the following is known:

Objective mag = 63x

Ocular mag =10x

Diameter of field of view when viewing specimen through occular = 320µm

Diameter of field of view when live viewing specimen on the screen = 100µm

What is the final mag of the rendered image on the screen?

This is not a homework question. The manufacturers specification for the degree of magnification that the camera and confocal (and obviously there is some) provide is unknown.

• what is the pixel size? what is sensor size? how many real-life microns fit in one micron of pixels is your magnification – aaaaa says reinstate Monica Jul 31 '15 at 22:03
• @aaaaaa live view on the screen is 920 W X 1200 H. No idea the size of the sensor unfortunately. – rhill45 Jul 31 '15 at 23:29
• What is the camera model? – aaaaa says reinstate Monica Aug 1 '15 at 0:17
• Usually the software that comes with the camera has the option of adding a scale bar. For all compound microscopes the final magnification = eyepiece magnification × objective magnification. The camera itself doesn't have any lens (AFAIK) and the image is not further magnified. However there are some settings that ensure that the digital image preserves all the optical information: the pixel size must be smaller than the inverse of 2.3-times the cut-off frequency [source]. – WYSIWYG Aug 1 '15 at 8:53
• @WYSIWYG if the image on the screen as compared to what your seeing through the occular is mag by a factor of 3,2, then the mag is different correct? – rhill45 Aug 1 '15 at 13:59

Assuming that the FOV that is captured by the CCD on the screen is 100µm wide as determined by the micrometer, and you are viewing the 920 pixel wide image on a standard 96 ppi monitor, the zoom would be approximately 2434 times.

$$\frac{920p}{96p/in}/100µm \approx 2434$$

Additionally, you should ensure that the minimum resolution on the micrometer is at least twice as large as each pixel on your microscope CCD.

The reason that the pixel size must be at least 2 times smaller than the minimum resolution present in the image is due to the Nyquist-Shannon sampling theorem.

This being said, all microscopes (and arguably all measurement devices) should be calibrated against a standard. This paper explains the usage of a standard to calibrate confocal microscopes.

A similar technique used to calibrate normal optical microscopes using a stage micrometer standard can be used if you do not possess such a standard. First calibrate the normal microscope, then image an identical sample using both microscopes in order to obtain the size of the field of view.

• This is great info but doesn't answer ?, I already did this. The fov is above. – rhill45 Aug 1 '15 at 13:56
• @rhill45 Sorry for initially misreading. Added my interpretation of the digital zoom. – March Ho Aug 1 '15 at 14:06