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Variable Focus Moire Lenses

Variable Focus Moiré Lenses

Continuous and exact variation of focal length within a wide focal length range

Aberration-free for monochromatic light

Suitable for high power applications

Scalable in aperture and spectrum (from UV to IR)

Thin and lightweight

Temperature-independent (between -20°C and 70°C)

Variable Focus Moiré Lenses consist of specially structured cascaded Diffractive Optical Elements (DOEs). These lenses are continuously adjustable over a wide focal length range by simply rotating the elements. Variable Focus Moiré Lenses exhibit aberration-free performance with monochromatic illumination and can be adapted for wavelengths from the UV to the IR. Typical applications include laser optical assemblies such as variable beam expanders, or as elements within a zoom lens, eliminating the need for complicated translating optomechanics.

Technical Diagram

Variable Focus Moiré Lenses
Rotating the 2nd element in the Variable Focus Moire Lens assembly with respect to the first provides continuous focusing of the light source. The assembly spans negative and positive focal lengths, over a range of ±50 diopters.


  How are Variable Focus Moiré Lenses manufactured?
The surface structure of individual Diffractive Optical Elements of a Variable Focus Moiré Lens are produced by standard photolithography techniques. The resultant pair of elements creates Fresnel zones that can be continuously adjusted to create a continuously variable focal length.
  What are the advantages of Variable Focus Moiré Lenses?

Variable Focus Moiré Lenses feature a pair of specially structured diffractive optical elements, fabricated via standard photolithographic techniques. These lenses also consist of a simpler design and construction than alternative liquid, photo-acoustic, or nanomaterial techniques. The simple construction also makes the Moiré lenses insensitive to changes in temperature and vibration resistant.

The plates are also thin, lightweight, and can be fabricated from a variety of materials including those which transmit in the UV or IR spectral regions. Focusing over a wide focal length range is achieved by a simple rotation of the plates, yielding aberration free spots when used with monochromatic illumination.

  Are there any disadvantages of Variable Focus Moiré Lenses?
  • Strong chromatic aberrations
  • Lens efficiency is reduced when its optical power is increased
  • Operates optimally only for a certain wavelength
  • Maximum aperture is limited (approximately 20mm)
  What is the efficiency of Variable Focus Moiré Lenses?

The first order diffraction efficiency n1 of a Moiré lens depends on the chosen twisting angle θ, resulting in the corresponding optical power:

n1 = (sinc (θ2))2 (1)

The total efficiency is a product of the diffraction efficiency and the transmission efficiency nt, which is approximately 96%. For a twisting angle of 90º, the diffraction efficiency is 81%, therefore the total efficiency is around 78%.

  How does Polarization affect the performance?
Variable Focus Moiré Lenses function independently of polarization.
  What specifications are required to create a custom Variable Focus Moiré Lens?

To create a custom Variable Focus Moiré Lens, the following is required:

  • Lens Size (Diameter, Square, etc.)
  • Clear Aperture
  • Maximum Thickness
  • Desired Focal Length Range
  • Operating Wavelength Range
  • Desired Efficiency for Maximum Optical Power
  What optical power range and Numerical Aperture (NA) does a Variable Focus Moiré Lens provide?
n1 = (sinc (θ2))2 (1)

Provided that the photolithographic processing unit of the DOE surface is in the wavelength range (which is true outside of the UV range), the optical power (D) of a Variable Focus Moiré lens can be calculated as follows:

D = θ (2)

Here θ, stands for the current twist angle of the DOEs and A denotes the clear aperture of the lens.

Equation 1 shows that the diffraction efficiency of the Variable Focus Moiré lens for a twist angle of ±90º (θ = ±π2) is higher than 80%. For this lens with an aperture of the optical power range is as follows:

D = ±12A = ±50 Dpt

This means that the optical power of the Variable Focus Moiré lens is inversely proportional to the aperture. The NA has a constant value throughout the modulation of its optical power (NA = 0.24 in example described above).

  What wavelengths are available?

Variable Focus Moiré Lenses can be manufactured for wavelengths from the UV through the IR. The Moiré pattern of the DOEs is required to be designed for a specific wavelength; maximum efficiency is achieved when the structure heights are equal to an integer multiple of the design wavelength (2π phase shift). The limiting factor in the DOE design is the transmission properties of the substrate. Fused Silica is commonly used for UV or visible applications, whereas Germanium is a common choice for IR applications.

Training Materials

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Moiré Theory

Adjustable refractive power from diffractive Moiré elements

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Moiré Demonstration

Demonstration of focus-tunable diffractive Moiré-lenses


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