spherometer

A spherometer is a precision instrument that measures the sagitta, the depth of curvature on a spherical or near-spherical surface. It consists of a central spindle with a fine-pitch screw, surrounded by three feet arranged in a triangle that rest on the test surface. As you turn the micrometer thimble, the spindle descends until it touches the peak of the curved surface, and the gauge reads the vertical displacement. This single measurement lets you calculate the radius of curvature without complex mathematics.

The classical spherometer has three legs spaced roughly 50 to 80 mm apart, with a dial or digital readout graduated to 0.01 mm or finer. When all three feet rest on a flat surface, the spindle reads zero. Place the instrument on a curved surface (lens, mirror, or polished component), lower the spindle until it just contacts the peak, and read the sagitta directly. The curvature radius R is then derived from the sagitta h and the triangle base dimensions. High-end versions use digital electronics with displays accurate to 0.001 mm, essential for precision optical work.

In lens grinding and polishing, the spherometer guards against over-correction and underbody degradation. Optical shops use it repeatedly as a surface approaches its target prescription to confirm that the radius matches the design specification, typically between 10 mm and several hundred millimeters. Mirror makers employ spherometers on parabolic and hyperbolic substrates to verify the overall sphere before the final figuring pass. The tool is also indispensable in quality control of finished optics: a deviation of even 0.1 mm in sagitta can shift lens focal length by several percent.

Common pitfalls and care

Operator error is frequent. The three feet must make firm, level contact with the work surface, or the reading becomes unreliable. Dirt or dust on the feet or spindle tip biases the measurement high. Applying excessive downward force on the micrometer knob can damage the fine screw thread or bend the frame. Temperature drift also matters: a 5 degree Celsius rise can expand the device enough to shift readings by 0.02 to 0.05 mm on tight tolerances. Always allow the spherometer and the test part to equilibrate to room temperature before measuring.

The name derives from the Greek sphaira, sphere, and metron, measure. The instrument has been in use since the early 19th century and remains largely unchanged in principle, though digital versions have replaced mechanical dial gauges in many laboratories. It occupies a unique position in optics: faster and simpler than full-surface interferometry, yet far more precise than a radius gauge or simple template fit. For production environments running hundreds of lenses per shift, the spherometer is often the only practical check between gross and finished specifications.