Real-time cell counting on a microscope is tedious. Using still images makes it much easier, but microscope cameras are expensive. I made a microscope adapter for my iPhone 5 out of laser-cut acrylic and double-sided tape. It's not perfect, but works well enough.

The rubber feet are McMaster part #95495K68, and the acrylic is cut from 1/4" and 1/8" nominal thickness sheets. The layers are stuck together with 3M 468MP adhesive sheets, but Thermoweb Peel-n-Stick or double sided tape would work just as well.

Laminate one sheet of 1/4" (nominal) thick acrylic with double sided tape. Do the same for a 1/8" thick sheet.

Adjust the eyepiece rings in the CAD file to fit the oculars of your microscope. Measure the diameter 1/4" in from the viewing side of the eyepiece, and use this as the inside diameter (ID) of all eyepiece rings.

Cut out the pieces as instructed in the CAD file, tape side down on the laser cutter. Some layers are made from 1/8", and others from 1/4". Going from the microscope side out, the thicknesses are 1/4", 1/4", 1/4", 1/4", 1/4" 1/8", 1/8". Once the pieces have been cut out, remove the backing from the tape of the outermost 1/8" piece. Scrape off the tape where it would touch the phone. Stick on the rubber feet on the appropriate rounded areas. Peel off the remaining backing and assemble.