An aspheric mirror can improve the quality of an optical system by reducing the complexity of the optical system. With the development of optical manufacturing and optical testing, the aspheric mirror is used commonly in optical systems. The aperture of the primary mirror increases to a few meters, or even dozens of meters. The aperture of the secondary mirror approaches one meter^[1–4].

Optical testing is a precondition of optical manufacturing. High-precision manufacturing of a convex aspheric mirror with a large aperture needs high-precision testing. The method used to test aspheric mirrors includes contour detection, non-aberration test, null lens test, stitching test, and so on^[5–12]. Contour detection is low precision and cannot be used to test a high-precision mirror. The non-aberration test can only be used to test a conic mirror and needs another mirror whose aperture is larger than the aspheric mirror^[12,13].

Since the optical mirror is fabricated based on the results of the test, the null lens defines the shape of the final optics. There is always a possibility that the null lens could be flawed, resulting in the final shape of the optics being incorrect^[5–12]. Two recent telescopes had their primary mirrors made to the wrong shape because of errors in the null lens: the Hubble Space Telescope and the European New Technology Telescope. If accurate testing of the null lens had been performed, the errors would have been discovered and corrected in the shop. Instead, the errors were not discovered until the finished mirrors were in their operational telescopes^[12,13].

In this Letter, we focus on testing an aspheric null lens in testing a large convex aspheric mirror. The large convex aspheric mirror is tested by an aspheric null lens. According to the parameter of the aspheric mirror, we design and manufacture an aspheric null lens that translates a flat wavefront to an aspheric wavefront to match the aspheric mirror and get the wavefront surface of the aspheric mirror by another traditional null lens. To calibrate the aspheric null lens, we design a computer-generated hologram (CGH) to test the aspheric null lens. The result of the aspheric null lens is 0.018λ RMS. The convex aspheric mirror is tested by the aspheric null lens and the test result is 0.030λ RMS.

Large aperture convex aspheric mirrors are always tested by a null lens. The principle of the null lens is that it translates a flat wavefront or spherical wavefront from the interferometry to an aspheric wavefront that matches the tested aspheric mirror. The standard lens for the interferometry can be spherical or flat. But a standard sphere cannot be aligned to the right position relative to the null lens. A standard flat interferometric lens is usually used to test an aspheric mirror with a null lens.

For a Φ338mm aspheric convex SIC mirror whose radius of curvature is 1024 mm, A2 equals 1.87×10−10, A3 equals 5.48×10−16, the deviate wavefront from the aspheric wavefront to its best fit sphere wavefront is 66.5728λPV is illustrated in Fig. 1.

For a large convex aspheric mirror, the density of the fringe exceeds the resolving power of the interferometer. A digital mask cannot be used to test the mirror. The mirror is not a conic mirror and cannot be tested by a non-aberration test. An aspheric null lens is designed and manufactured to test a large convex aspheric mirror. The optical layout and result of the design are illustrated in Fig. 2.

The parameter of the convex aspheric surface in the aspheric null lens about the radius of curvature is 535.439 mm, k equals −0.284091, A3 equals 2.072833×10−16, and A3 equals −4.456872×10−22. The deviate wavefront from the aspheric wavefront to its best fit sphere wavefront of the aspheric convex surface in the aspheric null lens is shown in Fig. 3. To manufacture the aspheric null lens another traditional null lens is designed. The optical layout and result of the design is shown in Fig. 4.

After manufacturing the aspheric null lens, the result of the aspheric null lens is tested by the traditional null lens is shown in Fig. 4. The result of the flat surface is shown in Fig. 5(a) and the result of the convex surface is shown in Fig. 5(b).

The simulated result of the null lens that uses the actual radius of curvature and thickness is shown in Fig. 6.

To calibrate the aspheric null lens, a CGH is designed. The optical layout of the calibration is shown in Fig. 7.

The precision of the CGH exceeds 0.01λ RMS. The test result of the aspheric null lens that is tested by the CGH is 0.018λ RMS is shown in Fig. 8.

The null lens is used to test the Φ338mm convex aspheric mirror whose radius of the curvature is 1024 mm and deviation from the aspheric wavefront to the best fit sphere wavefront is 66.5728λ. The optical layout of the test is shown in Fig. 9. The test result of the convex aspheric mirror is 0.030λ RMS, which satisfies the need for precision and is illustrated in Fig. 10.

This Letter provides a method to test an aspheric null lens, which is used to test a large convex aspheric mirror. A Φ338mm aspheric SIC mirror whose radius of curvature is 1024 mm and deviation from the aspheric wavefront to the best fit spherical wavefront is 66.5728λ is tested. Another traditional null lens is designed and manufactured to guide the manufacturing of the aspheric null lens. A CGH is used to calibrate the aspheric null lens. The test result of the null lens by the CGH is 0.018λ RMS. The test result of the mirror is 0.03λ RMS, which verifies that a large convex aspheric mirror that has a large deviation can be tested by an aspheric null lens. An aspheric null lens can be manufactured by another null lens and calibrated by a CGH.