*2.3. Hybrid Compensation Method*

Hybrid compensation is also an interference measurement technique to solve the shape measurement problem of the off-axis aspheric surface. When the aberration is larger than what a single CGH cannot be compensated, hybrid compensation is a suitable choice. In Figure 4, a fold sphere mirror was used to compensate most of the low-order aberration and a CGH was applied to compensate the residual aberration, which is still a null test system [18]. The function of each element in Figure 4 is similar to that illustrated in Figure 2 of Section 2.2.

**Figure 4.** Schematic diagram of the hybrid compensation method for off-axis aspheric surface.

The test result of hybrid compensation includes four parts, as seen in Equation (2),

$$Error\_{\text{total}} = Error\_{\text{TS}} + Error\_{\text{CGH}} + Error\_{\text{sphrev}} + Error\_{\text{asphric}} \tag{2}$$

In this equation, the definition of each sub-term is similar to that in Equation (1). The *ErrorCGH* from the CGH is very difficult to measure directly and can be estimated by an indirect method [19,20]. Similar to the first two methods (Sections 2.1 and 2.2), when *ErrorTS*, *ErrorCGH*, and *Errorsphere* are all small enough, the test result *Errortotal* is approximately equal to *Erroraspheric*. Otherwise, the error of these elements should be separately calibrated and then subtracted from the test result to obtain the error of the o ff-axis aspheric under testing.

In this measurement system, the fold sphere and CGH should be designed. According to laboratory conditions, the fold sphere is chosen by selecting the main parameters of the curvature radius and aperture. Meanwhile, the location position and fold angle of this fold sphere mirror should consider whether it will disturb the measurement. After choosing the fold sphere mirror and determining the geometrical parameters of its measurement system, the CGH can be designed. The CGH design processing is the same as that of the single CGH method, which is shown in Figure 3.

As shown in Figure 4, this hybrid compensation measurement system possesses four elements of the folded optical axis, resulting in a complex system that is characterized with huge di fficulty in adjusting. To reduce the di fficulty, the customized CGH is divided into multiple parts. In addition to testing the CGH, others are used to align between di fferent elements such as the interferometer and CGH, the fold sphere and CGH, and the aspheric and CGH.

The proposed three measurement methods that can all test the shape accuracy of conic o ff-axis aspheric surface belong to the null test. The auto-collimation method, which is the simplest technique with the simplest aiding element, is possessed of stronger generality. Single CGH and hybrid compensation both need customized CGH, so they have less generality. The customized CGH, which is a di ffractive element, needs long and expensive preparation. However, these two methods can measure more surface types with the assistance of adjustment marks, resulting in a wider range of application.
