Controlling light with freeform multifocal lens designed with supporting quadric method(SQM)

Area of Science:

• Optics
• Optical Engineering
• Freeform Optics Design

Background:

• The Simultaneous Multiple Surface (SQM) method is a versatile tool for designing freeform optical elements.
• Its application in lenses, mirrors, and diffractive optical elements is increasing, but theoretical and performance aspects require further investigation.
• Freeform optics are crucial for advanced optical systems requiring complex light manipulation.

Purpose of the Study:

• To theoretically investigate plano-freeform refractive lenses designed using the SQM methodology.
• To analyze the performance of SQM-designed lenses for transforming collimated beams into specific irradiance distributions on a flat screen.
• To explore the multifocal nature and subaperture characteristics of SQM-designed lenses.

Main Methods:

• Theoretical investigation of plano-freeform refractive lenses designed with the SQM.
• Analysis of lenses transforming a uniform collimated beam into a prescribed irradiance distribution.
• Derivation of the Eikonal function for SQM-designed lenses.
• Numerical performance analysis of a proof-of-concept lens.

Main Results:

• SQM-designed lenses function as multifocal elements segmented into subapertures.
• These subapertures, composed of hyperboloid patches, provide precise control over irradiance distribution.
• Two design variations are possible, including a concave lens configuration.
• A numerical example demonstrates the transformation of uniform light into a detailed image (A. Einstein) across approximately 38,000 pixels.

Conclusions:

• Plano-freeform refractive lenses designed with SQM exhibit multifocal properties enabling accurate irradiance control.
• The SQM methodology is effective for designing complex freeform optics for high-pixel-count display applications.
• The derived Eikonal function aids in understanding the light propagation through these novel optical elements.