# Measuring minimal and maximal microscope magnification and zoom ratio

Magnification ratio is one of many parameters to describe optical instrument – microscope in this case. Magnification ratio usually comes along with zoom range. These terms are often being misused. In this post I will measure zoom range and magnification ratio of monocular video microscope lens and stereo inspection microscope (Konus #5424) head.

Despite being different kind of optical instruments they have similar magnification ratios, so it’s fair to compare them.

### Measurement

Let’s mount C1 camera on a lens and take some pictures of a known object at minimal and maximal magnification.

Two different rulers will be used:

- Larger one is 50cm steel ruler
- Smaller one is microscope slide 5mm with 0.01mm marks

I will use these pictures to measure view field dimensions. Also to be noted that video microscope uses 0.5x adapter tube.

Declared min magnification: (0.7x * 0.5) 0.35x ->13mm(H) x 7.3mm(V)Declared max magnification: (4.5x * 0.5) 2.25x ->2mm(H) x 1.1mm(V)

### Math – zoom ratio

Quickly calculate diagonal viewable image size at min and max magnification:

SQRT(13^2 + 7.3^2) =14.9mmSQRT(2^2 + 1.1^2) =2.3mm

And now we can find zoom ratio:

Theoretical: (4.5*0.5) / (0.7*0.5) =6.4xZoom ratio: 14.9 / 2.3 =6.5x

So stated magnification ratio is pretty legit. Good to know that manufacturer does not lie.

For reference I also measured trinocular microscope viewable image size at minimal and maximal magnification ratio. Please note that this time I measured rulers by eye and projected image is disc instead of being rectangular.

Declared min magnification 0.7x: D=33mmDeclared max magnification 4.5x: D=4.5mmZoom ratio: 33/4.5 =7.3x

While specified parameters are the same magnification range is slightly wider than previous optical instrument.

### Math – magnification

While we can’t measure stereo microscope magnification (don’t have projected image dimensions), it is pretty easy to calculate this parameter for lens mounted on a camera. To calculate this parameter we need to know used camera sensor dimensions. Good to know that C1 camera has known sensor dimensions.

Sensor size horizontal:5.07mm(H)Sensor size horizontal:3.38mm(V)Sensor size diagonal: SQRT(5.07^2 + 3.38^2) =6.09mm

Also let’s take into account that camera does not use full sensor.

Pixel dimensions: 2.2µm x 2.2µm (square pixels) Frame size: 1920 x 1080 True frame size horizontal: 1920 * 2.2µm =4.224mmTrue frame size vertical: 1080 * 2.2µm =2.376mmTrue frame size diagonal: SQRT(4.224^2 + 2.376^2) =4.85mm

Now when we have source and destination image sizes let’s normalize them to have nice magnification ratio

Min magnification: 4.85 / 14.9 = 0.33 =** 1:3 **Max magnification: 4.85 / 2.28 = 2.12 = **2:1**

Simplified animated illustration shows projected image size variations.

### Compare results

To compare viewable area of both microscopes I provide you drawing.

While both compared microscopes have specified range of 0.7x-4.5x they have slightly different optical parameters. At a first glance video microscope has smaller view area, but it might be deceptive conclusions. Actually being C-mount it is suitable for larger sensors. How big? It might be between 1″ and 1/2″.