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I'm trying to measure water elevation as a function of distance in a water tank, viewed through the glass wall, as shown here:

tank

The height variations that's of interest to me is very small. Would anyone know of a lens that can be placed in front of a camera to stretch the image vertically? This will help enhance the vertical resolution of the photo. Other suggestions are also welcome.

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How about this?

enter image description here

Photo 1. Inclined tank level scale.

The inclined scale means that graduations can be spread more widely for ease of reading. For example, if 1 mm resolution is required and the line rotated by 84 degrees the 1 mm marks stretch out to 10 mm making it much more easy to read and interpolate. cos(84°) = 0.1. This effectively stretches the vertical resolution as required in the question but without the use of a lens.

It's not obvious from the question whether an automated vision system is to be used but either way this should make reading the level somewhat easier.

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Assuming you need to gather displacement data from every position along the horizontal dimension of the tank simultaneously, you may be looking for a cylindrical lens, which focuses light onto a line, as noted in the link. With a proper lens setup, you should be able to change the aspect ratio of the field of view and capture greater resolution along the vertical without affecting the horizontal.

It might be worth putting a uniform, high-contrast background behind the tank and using plenty of illumination of both the water and background to assist with accurate measurements.

An alternate method to consider is interferometry, and it may offer greater accuracy than imaging devices. From the link (emphasis mine):

Interferometers are widely used in science and industry for the measurement of small displacements, refractive index changes and surface irregularities.

I am unsure how to set up an interferometer to measure displacements in water height, however.

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