Extreme-depth-of-focus imaging with a flat lens
Sourangsu Banerji, Monjurul Meem, Apratim Majumder, Berardi Sensale‐Rodriguez, Rajesh Menon
Abstract
A lens performs an approximately one-to-one mapping from the object to the image plane. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity, and weight of imaging systems. Here we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus by over 4 orders of magnitude. Using such a lens, we are able to maintain focus for objects that are separated by as large a distance as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>∼</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>6</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> in our experiments. Specifically, when illuminated by collimated light at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.85</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>µ</mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , the MDL produced a beam, which remained in focus from 5 to 1200 mm. The measured full width at half-maximum of the focused beam varied from 6.6 µm (5 mm away from the MDL) to 524 µm (1200 mm away from the MDL). Since the side lobes were well suppressed and the main lobe was close to the diffraction limit, imaging with a horizontal × vertical field of view of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>40</mml:mn> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>30</mml:mn> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> over the entire focal range was possible. This demonstration opens up a new direction for lens design, where by treating the phase in the focal plane as a free parameter, extreme-depth-of-focus imaging becomes possible.