Diffractive optical elements for 3D light field distributions

By Dr. Shima Gharbi Ghebjagh

Optical Engineering Group (Fachgebiet Technische Optik)

A structure and method for generating three-dimensional (3D) light structures has application in a number of modern technologies like illumination and image processing in optical microscopy, optical lithography and microfabrication, as well as positioning and manipulation of multiple micro-particles in 3D space. Recent advances in diffractive optics theory and technology have made 3D beam splitting and shaping a valuable resource for the optics community. The critical issues are high diffraction efficiency and uniform power distribution among the diffraction orders.

Diffractive optical elements (DOE) consist of transparent substrates with imprinted micro-patterns perturbing the phase of the electromagnetic waves to allow interference [1]. They allow e.g. the splitting of a single beam from a coherent source (laser), creating a specific output pattern and adaptation of wavefronts to desired functionalities using the effects of diffraction. A Fresnel zone plate (FZP), is a diffractive lens consisting of annular zones, which focus the wave through constructive interference of diffracted fields into a focal point.

In order to satisfy the requirements of parallel processing efficiency, we proposed and demonstrated a novel multi-focal diffractive lens that generates a required number of highly efficient axial foci with uniform, predetermined intensity. The design is accomplished by dividing each period of the conventional FZP into several areas with equal widths, each having a different phase value with an emphasis on the optimization of the phase values to acquire the best possible uniformity and efficiency for the focal spots. This way the element can replicate a single focus spot into several defocused planes along the propagation axis. By overlapping the phase structures of the multi value phase diffraction grating a 3D array of uniform focal spots in transverse and axial directions can also be generated [2].

Fig.1 (a) Multi focal diffractive lens. (b) Intensity distribution of a coaxial array of focal spots, (c) Intensity profile of the generated focal spots along the optical axis

Diffraction based engineered and shaped beams have recently been demonstrated for precise 3D position information transfer at the microscale as well as optical microscopy and micromanipulations [3]. Orbital angular momentum (OAM) is an advantageous concept of optical vortex beams, which enhances the information carrying capacity of the photons. An optical vortex is a type of structured light beam with a doughnut shape lateral intensity that carries OAM. Headed for improved techniques in 3D optical manipulation and imaging, we implemented a spiral phase into the phase structure of a Multi-focal diffractive lens, and by superposing two spiral structures with different degrees of chirality, we established a method for the generation of axial arrays of structured optical vortex beams known as petal-like beams and optical ring lattices. The design scheme is based on implementing a four region spiral multi-value zone plate with two different topological charges in each region in tandem, to provide a constructive interference among the diffracted beams. This technique eliminates the need for complex interferometric set ups, which are very sensitive to experimental errors. The generated structures can be rotated with quantitative control around the beam axis by introducing a transverse angular shift between the two composited spiral multi-focal diffractive lenses. The inherent properties of the rotatable arrays of the generated structured light beams suggest that they can be utilized to improve the 3D optical manipulation and molecular imaging [4].

Fig. 2. Array of structured optical beams as (a) optical vortices, (b, c) rotatable petal-like beams and (d) optical ring lattices with different degrees of OAM based on the diffraction orders.

The simultaneous control and manipulation of micro-particles in 3D working space and the ability to image multiple moving objects simultaneously, requires in the first place the generation of multiple focal spots and in continuation the focus tuning functionality and adjustment of the focus positions along the propagation direction. Adaptive lenses are a current topic of research because of their capability to provide compact and flexible optical systems, and Alvarez-Lohmann lenses are important kinds of adaptive optical elements, in which the focal length tuning is achieved by slightly shifting two combined cubic elements with respect to each other [5]. Based on the concept of Alvarez-Lohmann lenses, we designed a tunable multi-focal diffractive lens, which generates multiple focal spots along the optical axis and provides precise adjustment of the focus positions along the propagation direction. This way, the distance of the focal spots can be tuned accurately, which paves the way for simultaneous and dynamic 3D manipulations and 3D multi-focal fluorescence microscopy. We utilized a specific combination of two identical multi-phase value basic grids, and by applying a mutual rotation between the two diffractive elements, the spherical phase of the tunable multi-focal lens is generated and a continuous adjustment of the optical power and therefore a dynamic tuning of the foci distances is achieved [6].

Fig. 3. (a) Sample phase profiles of two multi-value phase diffractive grids generating a tunable multi-focal lens phase (b) Combining the basic grid pair and increasing the mutual rotation angle modifies the focal spot array locations along the optical axis.

Light sheet fluorescence microscopy (LSFM), as a minimally invasive optical imaging technique, utilizes two object lenses with orthogonal optical pathways to confine illumination to a single, thin plane. LSFM provides inherent optical sectioning without over exposing the sample and reduces the photo-damage [7]. A combination of pipe based bio reactors and multi-plane illumination in LSFM provides a robust scanning, study and characterization approach for 3D cell cultures. This method excludes the need for scanning in the illumination and detection arms, reduces the aberrations due to mechanical movements and has the potential for particle speed measurements. The method for generating multiple light sheets with uniform intensity along the guiding tube is to implement a linearly modulated multi-focal diffractive lens in combination with a cylindrical lens based on a detour phase approach. Taking advantage of the order dependent focusing and steering functionality of the designed system, focal spots are generated and oriented along a desired line passing through the specimen tube. The system principally provides dedicated simultaneous 3D illumination and imaging [8].

Fig. 4. (a) Schematic of the sample guiding tube illuminated by multiple light sheets (b) equal intensity multiple light sheets shifted in z direction.


  1. S. Sinzinger and J. Jahns, “Microoptics”, John Wiley & Sons, (2003), 2nd edition.
  2. Sh. Gh. Ghebjagh, D. Fischer, S. Sinzinger, "Multifocal multi-value phase zone plate for 3D focusing," Appl. Opt. 58, 8943-8949 (2019).
  3. Sri Rama Prasanna Pavani and Rafael Piestun, "High-efficiency rotating point spread functions," Opt. Express 16, 3484-3489 (2008).
  4. Sh. Gh. Ghebjagh, S. Sinzinger, "Composite spiral multi-value zone plates," Appl. Opt. 59, 4618-4623 (2020).
  5. A. W. Lohmann and D. P. Paris, "Variable Fresnel Zone Pattern," Appl. Opt. 6, 1567-1570 (1967).
  6. Sh. Gh. Ghebjagh, A. Behrens, P. Feßer, S. Sinzinger, "Tunable multi-focal diffractive lens," submitted to OSA Imaging and applied conference, 2021.
  7. M. Hofmann, Sh. Gh. Ghebjagh, K. Lemke, S. Sinzinger, "Multi-sheet excitation and imaging of flow driven samples in a LSFM with a modified multi-focal diffractive lens," submitted to OSA Imaging and applied conference, 2021.