I were assembling a home-optometry kit, I would use adjustable oil lenses and a laser pointer. The speckle pattern of the laser dot is affected by whether the observer is myopic or hyperopic. Adjust the oil glasses until, when moving your head, the laser speckle dots do not appear to move. If they move opposite to your head motion, make the lens diopter more negative, and if they move in the same direction, make the lens diopter less negative.
After determining exact spherical diopter, then test for astigmatism by spinning a set of parallel black lines on a white field, and parallel white lines on a black field. Or just look at a printout of an astigmatism dial chart.
After determining exact spherical diopter, then test for astigmatism by spinning a set of parallel black lines on a white field, and parallel white lines on a black field. Or just look at a printout of an astigmatism dial chart.