## Technical tips – Methods to reduce zero-order effect

__Introduction__

what is zero-order in terms of diffractive optics?

Zero-order is the part of the energy from incident beam going through the diffractive optical element (DOE) without being “diffracted”, meaning part of the incident beam “obeying” only geometrical ray optics (reflection & refraction) equations.

Although in some cases the zero-order is part of the designed image (array of spots), there is still an issue with its energy variation compared to the design (nominal). Trying to bypass this issue can result in complex optical setups or abandoning the project all together due to higher costs or insufficient performances

__The problem__

In the real world, nothing is perfect, and zero order will be present (to some extent). Zero-order “shooting” out of the uniformity spec of the image can cause serious problems in many any applications.

This mainly happens due to three types of effects:

- Design-related effects:
- The validity of scalar theory for features (diffractive microstructures) smaller than 5λ

- Fabrication-related effects:
- Fabrication errors (etch depth errors and lateral misalignment)
- The steepness of side walls
- Surface roughness

- Operation & integration-related effects
- The spectral width of the source
- The difference between the wavelength of the light source vs. optimal design of the DOE
- The collimation of source
- The incidence of the input beam (shadowing effects)
- The polarization state of the source (only relevant with item (1).a)

__Solutions__

We present here several alternatives to suppress the zero-order, each one with its advantages and disadvantages:

- Using Non-collimated incident beam
- By inserting a non-collimated/diverging input beam to the DOE, the zero-order will continue diverging like the source, thus spreading over a large region, “smoothing out” the hot-spot. This technique works only for far-field applications, so the addition of a focusing lens is prohibited (or zero-order will be focused as well). In addition, a new DOE design with internal diffractive lens might be needed.

- Zero-order reduction by special diffractive design
- As most DOEs are designed using Iterative-Fourier-Transform-Algorithm (IFTA) it is possible to give the zero-order optimization parameter larger weight in the overall merit function, over uniformity, efficiency, etc.

- Three phase level diffractive structures instead of two
- The introduction of a third phase level to the original binary grating profile can significantly reduce the design sensitivity to profile depth error (this translates into lower sensitivity to spectral width resulting zero-order).

- Lateral shifting of the desired output image relatively to zero-order – Adding a diffractive prism
- By including diffractive micro prisms in the design, the possible energy of the zero order (i.e. 1-2%) continues on the optical axis, while the desired image is deflected in a certain angle according to the diffractive micro prism array. This solution will show lower sensitivity to misalignment compared to other alternatives.

- Focal shifting of the desired output image relatively to zero-order – Adding a diffractive (Fresnel) lens
- By including a Fresnel type of lens the possible energy of zero order (i.e. 1-2%) spreads out and is evenly distributed over the entire region and appears as a small background noise. Usually, we choose the design so that the desired image will be before the original focal plane, thus, the zero order will be at focus at the focal plane (It is also possible to move the zero order to other plane and leave the image plane at the original EFL of the system).

- Mechanical mask to block the zero-order at an intermediate image plane – UDOB module
- This method inserts a real engineered aperture in a virtual intermediate focal plane that physically blocks (by reflection) the zero-order. This is often used to also block higher diffractive orders and stray light.

- Double sided DOE in Holo/Or’s homogenizer type products (HH / RH / XH)
- Holo/Or developed a new class of diffusers/homogenizers with enhanced performance referred to as the high homogeneity series (Homogeneity can be defined as the average intensity over an area unit). Its advantages are higher homogeneity, and lower zero order. This DOE design includes two diffractive surfaces. The first decreases the coherence of the incident beam and the second surface shapes the beam.

__Conclusions__

In Holo/Or we can offer all of the above different solutions for customers that require a very small zero-order or precise values in a specific range.

These solutions are also good for customers that want to use the same product for wavelengths over a spectral range of about +/-10% (or even more, depending on the set-up and the type of solution).

The table below summarizes the different alternatives to handle the zero-order effect:

Solution |
Advantage |
Disadvantage |

Using a Non-collimated incident beam |
Might not require alterations to the DOE | Addition of a diffractive lens to diffractive design adds its own manufacturing tolerances, otherwise, output shape & transfer region increases, and this can cause overlap of spots if used with multi-spot |

Zero-order reduction by special diffractive design |
Simplest integration | Limited affectivity (relevant for small angle and small number of spots for Multi-Spot) |

Three level diffractive structures instead of two |
Cheap relative to multi-level solutions (8 & 16) | Useful only for multi-spectral applications |

Lateral shifting of desired output image relatively to zero-order – Adding diffractive prism |
Lower sensitivity to centration compared to solutions with diffractive Fresnel lens | Output image is laterally shifted compared to the optical axis. More expensive than binary (2-level) DOE due to the addition of a multi-layer micro prisms. Limited to relatively small angles applications |

Focal shifting of desired output image relatively to zero-order – Adding diffractive (Fresnel) lens |
On axis solution. Can achieve higher efficiency compared to other solutions | Centration is more important. More expensive than binary (2-level) DOE due to the addition of a multi-layer Fresnel lens |

Mechanical mask to block the zero-order at an intermediate image plane – UDOB module |
Blocks more than 99% of the zero-order | A full solution in a multi-elements module instead of a single DOE |

Double sided DOE |
Simple to design. Significantly reduces zero-order | More expansive due to second diffractive surface. Limited to homogenizer type products |

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