Lesson 5 – Spherometers and Radius Measurement
What You Will Learn
- Describe how a spherometer measures sag over a known aperture.
- Explain how sag measurements are converted into radius of curvature.
- Select the proper ring reference diameter for convex and concave surfaces.
- Recognize why long, shallow radii are more difficult to measure accurately.
- Calibrate and verify a spherometer before use.
- Identify common setup errors that can affect radius measurements.
- Explain how cleanliness and handling influence measurement quality and cosmetic condition.
Lesson Video
Video Placeholder: Insert the narrated lesson video for this metrology topic here.
Spherometer Function
A spherometer is a precision contact instrument used to measure the curvature of spherical optical surfaces. The instrument consists of three fixed support points arranged in a circle and a central measuring probe that contacts the optic. When the spherometer is placed on a curved surface, the center probe moves relative to the support ring. This movement represents the sag, or sagitta, of the surface. Because the support points are positioned on a known diameter, the measured sag can be mathematically converted into radius of curvature. For this reason, spherometers are commonly used throughout optics manufacturing to monitor grinding and polishing progress, verify generated radii, and support process adjustments.
Spherometers provide rapid shop-floor measurements without requiring large optical test equipment. Although they are extremely useful, they provide only an indirect radius measurement. The instrument directly measures sag; the radius must then be calculated from the measured sag and the known ring diameter.
Radius Calculation Fundamentals
The radius of curvature is calculated using the measured sag and the effective aperture diameter of the spherometer. Even very small changes in sag can produce significant changes in calculated radius, especially when measuring long-radius surfaces. As the radius becomes longer and the surface becomes flatter, the sag value decreases dramatically. In some cases, the sag may only be a few micrometers. Because the measured sag is so small, even slight errors caused by contamination, poor zeroing, or improper seating can produce large errors in the calculated radius. Steeper surfaces generally produce larger sag values and are therefore easier to measure accurately. Long, shallow radii require greater care, repeat measurements, and careful verification of instrument calibration.
Convex and Concave Measurements
The support ring geometry used in the radius calculation depends on whether the surface is convex or concave. For convex surfaces, the inside diameter of the spherometer support ring is typically used in the radius calculation. For concave surfaces, the outside diameter of the support ring is generally used. Selecting the wrong reference diameter produces an incorrect radius even when the sag measurement itself is accurate. Technicians should always verify the required calculation method, instrument documentation, and shop procedures before recording results. In addition, the optic must be positioned so that all support points contact the surface evenly. If one support point does not contact correctly, the spherometer may rock or tilt, resulting in unstable or incorrect measurements.
Calibration and Zero Verification
Before measuring an optic, the spherometer must be calibrated or zeroed against an appropriate reference standard. Calibration establishes the relationship between probe movement and the actual sag value. Many shops use calibrated optical flats, reference spheres, or certified standards to verify instrument performance. Operators should confirm that the instrument reads correctly before beginning measurements, particularly when tight radius tolerances are specified. A reliable zero is essential. An incorrect zero offset affects every subsequent measurement and can result in significant radius errors. Repeating measurements several times and comparing results helps confirm that the setup is stable and repeatable.
Cleanliness and Cosmetic Risk
Because a spherometer directly contacts the optical surface, cleanliness is critical. Dust, abrasive residue, fingerprints, or contamination trapped beneath the support points can affect the sag reading and may damage the optic. Operators should inspect and clean the support ring, center probe, and optical surface before every measurement. Contact points should be examined periodically for wear, damage, or burrs that could scratch polished surfaces. Careful placement and removal of the instrument helps reduce cosmetic risk. The spherometer should be lowered gently onto the optic and lifted vertically after the measurement is complete. Sliding the instrument across the surface should always be avoided.
Shop Floor Practice
Review a drawing or inspection plan and identify the required radius specification. Select the appropriate spherometer and verify that the instrument range is suitable for the surface being measured. Confirm calibration, clean all contact points, and record multiple measurements to verify repeatability. Compare measured values to drawing requirements and discuss how cleanliness, zero offset, incorrect ring diameter selection, or operator technique could affect the final result.
Knowledge Check
- What quantity does a spherometer directly measure?
- Why is the support ring diameter required for radius calculations?
- Which ring diameter is typically used when measuring convex surfaces?
- Why are long, shallow radii more difficult to measure accurately?
- Why must a spherometer be calibrated before use?
- How can contamination affect both measurement accuracy and optical quality?