n1 = (sinc (θ⁄2))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⁄Aπ (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 = ±π⁄2) is higher than 80%. For this lens with an aperture of the optical power range is as follows:
D = ±1⁄2A = ±25 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).
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
Variable Focus Moiré Lenses function independently of polarization.
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.
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 (θ⁄2))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 45º, the diffraction efficiency is around 65%, therefore the total efficiency is approximately 62%.
- 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)
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.