Modern imaging optics, especially free-form optics, have boosted high-performance and compact imaging systems in a wide range of applications [1], [2], [3], [4], [5], [6], [7]. Nevertheless, there are still many challenges in the implementation of aspheric optics throughout their design, fabrication, testing, and assembling processes [8], [9]. The concurrent engineering concept reveals the importance of the testing process within the entire production line, as it could provide valuable feedback to the other processes [10]. However, surface testing for aspheric optics is generally difficult and sophisticated in conventional methods [11], [12] because their shapes are sometimes non-spherical, non-rotationally symmetrical, or even multi-axis. Wavefront detection is a non-contact method and measures the surface profile of the optics under test through its equi-phase surface’s slope or optical path length differences of its transmitted or reflected light beam. Wavefront aberration coefficients could be conveniently represented with the Zernike polynomials [13], [14], [15].

Standard wavefront detection techniques include optical interferometers and wavefront sensors such as the Hartmann wavefront sensor (HWFS) or the Shack–Hartmann wavefront sensor (SHWFS). Optical interferometers could achieve high-precision wavefront measurements. However, they usually require etalon or computer-generated hologram as the compensator when testing aspheric optics, which is generally high cost, difficult to be aligned, and sensitive to environmental changes [15], [16], [17], [18]. The HWFS measures the wavefront by detecting the wavefront slopes with a pinhole array and an imaging sensor behind the array [19], [20]. Although the wavefront measurement precision is relatively low, the HWFS is low-cost and robust. The SHWFS replaces the pinhole array in HWFS with a microlens array, which could provide higher accuracy and more energy efficiency in the wavefront measurement [21]. Compared to the SHWFS, the most important advantage of the HWFS is its low cost and easy implementation.

Because of its simple and low-cost system setup, the HWFS is widespread in wavefront measurement applications. Unfortunately, conventional HWFS suffers from the well-known trade-off between the dynamic range and spatial resolution [22], [23], [24]. Serial digital micromirror devices (DMD) raster scanning provides an option to deal with this trade-off [25]. However, its DMD has to be placed at the entrance pupil of the CCD so that the energy concentration on the CCD is variant while adjusting spatial resolution through combining adjacent micromirrors. It is not economically suitable for large field-of-view (FOV) measurements due to the DMD size limit and alignment problem.

Moreover, the cost of data acquisition and storage for large field-of-view wavefront measurement is also significant [26], [27]. As we know, resolution enhancement resorting to scanning acquisition approaches has already been verified [28], [29]. Their most essential feature is to exchange the acquisition rate for better performance. Previously, we proposed a raster scanning Hartmann wavefront sensor (RS-HWFS) with a two-dimensional translation stage to solve similar issues in HWFS. RS-HWFS decouples the dynamic range and spatial resolution to achieve high spatial resolution, extensive dynamic range, high sensitivity, and large FOV simultaneously [30]. In the RS-HWFS, the wavefront slope was measured by tracking the diffraction spot of a single sampling pinhole with an imaging sensor behind it. However, to acquire large FOV or high spatial resolution wavefront measurement, the scanning acquisition is sometimes time-consuming.

In this paper, we propose a sparse scanning HWFS (SS-HWFS), which allows the input with a compressed aperture for the reconstruction. While using a similar setup as the RS-HWFS, the SS-HWFS performs random sub-sampled data acquisition and then reconstructs the entire FOV wavefront with compressed sensing (CS) technique by assuming that the wavefront is sparse in the Zernike domain. Note that the CS is an attractive technique that enables recovering a sparse signal beyond the Shannon–Nyquist theorem and has been successfully utilized in HWFS for reducing unnecessary acquisition [31], [32], [33].

By combining the scanning approach and the compressed aperture reconstruction, the SS-HWFS could achieve better spatial resolution and dynamic range simultaneously, as well as large FOV and relatively quick data acquisition. Moreover, the SS-HWFS could provide a relatively low-cost and robust alternative non-null solution for detecting wavefront aberration in static optics because of the simple setup. Our proposed method is applicable to both Hartmann wavefront sensors and Shack–Hartmann wavefront sensors. It is possible to replace the single pinhole with a single micro-lens to increase energy efficiency, which, however, increase the cost and alignment difficulties.