## 1 Introduction  
Diffractive optical elements (DOEs) have general advantages in comparison to their refractive counterparts such as being basically flat, thin, lightweight, and inexpensive when mass-produced. However, they exhibit large chromatic aberration (e.g., in diffractive lenses, approximately one diopter of axial chromatic aberration for every three diopters of power) and frequently low diffraction efficiency [1]. [PERSON] and [PERSON] [1] and [PERSON] and [PERSON] [2] simultaneously and independently introduced DOEs with multiwavelength optical path-length transitions between adjacent facets, called harmonic and multiorder diffractive lenses, respectively. These lenses have hybrid properties of both refractive and diffractive lenses, and they have a common focus for a number of discrete wavelengths. [PERSON] and [PERSON] [1] measured the modulation transfer function (MTF) when a harmonic diffractive lens was used for imaging under either monochromatic or white light illumination. They showed that a lens with 10 wavelength phase steps approached diffraction limit behavior across the visible spectrum. [PERSON] and [PERSON] [2] used multiorder diffractive lenses to design an achromatic diffractive singlet. The performance of such a lens was illustrated through MTF and Strehl ratio measurements as a function of wavelength. By 1995, advances in fabrication techniques of diffractive elements allowed development of the ideas proposed in these works. Multiorder DOEs have some constraints though. For example, higher-order structures restrain their off-axis performance. Because of the greater height at the edges of each facet, an effect appears, referred to as shadowing [3; 4]. Even for diffraction angles of a few degrees, the wavefront emerging from the blazed structure has small gaps introduced by the facets that affect the diffraction efficiency of the DOE [4]. This inconvenience can be overcome with the modern technology of liquid crystal (LC) displays. The evolution of diffractive components experienced a significant advancement with the development of electrically addressed liquid crystal spatial light modulators (LC-SLM), capable of implementing a variety of programmable DOEs. Phase-only LC-SLM with a phase modulation depth larger than \(2\pi\) radians is nowadays commercially available based on LC on silicon (LCoS) technology working on a reflection regime. A parallel-aligned LCoS display reaching a dynamic phase range of \(4\pi\) radians for \(\lambda=454\) nm has been used to implement second-order diffraction DOEs, such as diffractive gratings and diffractive lenses, with some advantages in terms of resolution and diffraction efficiency compared to conventional first-order DOEs [5]. An LCoS-SLM initially designed to operate in infrared provides unusually large phase modulation depths in the visible band range, for instance, from \(6\pi\) radians in the red region to \(10\pi\) radians in the blue region [6]. This performance allows the display of a blazed diffractive grating with a reduced chromatic dispersion. The discrete pixel structure [7] and the quantization of the available phase levels [8] of LC-SLM introduce some limitations in the implementation of DOEs on such displays. The spatial resolution of the screen may limit efficient encoding of diffractive lenses. On the one hand, low-resolution lenses implemented in the pixelated structure of LC-SLM introduce an inherent apodizing effect on the system point spread function (PSF). Apodization diminishes the secondary maxima of the PSF, but it increases the width of the central lobe [9; 10]. These effects become more severe as the width of the pixel increases or as the focal length of the lens decreases. However, novel LCoS displays with a smaller pixel size and larger fill factor reduce the apodizing effect of the pixelated structure as they better approach the ideal continuous lens function.