Abstract
In this study the methods of three-dimensional (3D) wavefront intensity modulation by employing contrast-inverted holography, previously introduced as Gabor inverted holography, are further investigated. The present study provides the recipes for creating 3D wavefront intensity modulations using phase-only and amplitude-only modulators and compares the results. The 3D wavefront modulation using spherical waves is also demonstrated, and the miniaturization of 3D intensity beams is discussed; it is shown that both the resolution and the size of the created 3D structures are ultimately given by the wavelength of the employed radiation. The manuscript also addresses the quality of the formed 3D intensity curves and determines the parameters that provide the best smooth appearance of the 3D curves. The presented methods of 3D intensity wavefront modulation can be realized for all kinds of waves: light, X-ray, electron, etc, provided the modulator can be manufactured for the corresponding wavelength. The methods of 3D intensity wavefront modulation can be applied in various techniques: lithography, micro-robotics, particle trapping, etc.
Highlights
Wavefront Modulation and BeamWavefront modulation techniques utilize optical schemes, where an optical element transforms the distribution of a passing wave into a pre-defined wavefront distribution at some distance behind the optical element
Holography [1,2] is a technique that is widely employed for wavefront modulation, in particular by using so-called computer-generated holograms (CGH) [3,4]
Three-dimensional wavefront intensity modulation using an amplitude-only modulator was previously discussed in great detail in the original publication [7], and it is not discussed in this paper
Summary
Wavefront modulation techniques utilize optical schemes, where an optical element (modulator) transforms the distribution of a passing wave into a pre-defined wavefront distribution at some distance behind the optical element. For two-dimensional (2D) wavefront modulation, a modulator’s distribution can be calculated by applying an iterative phase retrieval algorithm, originally proposed by Gerchberg and Saxton [10] as follows. A wavefront is propagated back and forth between the two planes: the modulator and the image plane, and at each plane, a constraint is applied. The wavefront must be a phase- or amplitudeonly distribution depending on the modulator type. The wavefront must exhibit the pre-designed 2D distribution. A modulator distribution found by an iterative approach [11] allows wavefront modulation into a pre-designed 2D distribution in one plane
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