JTu3A.3.pdf
`
`Design and Fabrication Congress 2017 (IODC,
`Freeform,OFT) © OSA 2017
`
`Miniature Camera Lens Design with a Freeform Surface
`
`Yufeng Yan and Jose Sasian
`University of Arizona, College of Optical Sciences, 1630 East University Boulevard, Tucson, Arizona, 85721
`yyan@optics.arizona.edu, jose.sasian@optics.arizona.edu
`
`Abstract: We present a miniature camera lens design using a freeform surface based on the pedal
`curve to the ellipse and compare its optical performance to the conventional design with a standard
`even aspheric surface.
`OCIS codes: (220.3620) Lens system design; (080,4225) Nonspherical lens design
`
`1. Introduction
`Camera lens designs for mobile platform electronics applications such as cell phones and tablets have been rapidly
`developed in the past decade. Although these miniature cameras in mobile devices are becoming ubiquitous in our
`daily lives, better optical performance is always demanded. To achieve good optical performance for the miniature
`cameras, aspherical surfaces are extensively used during the lens design. However, the performance of the miniature
`cameras designed with conventional aspherical surfaces is approaching a limit. While lens designers are still pushing
`the limits of their designs with conventional even/odd aspherical surfaces, a more efficient surface description is
`desirable for improvement. A recently published paper [1] introduced a freeform surface that combines base
`surfaces of the pedal curve to the ellipse for light illumination control. In this summary, we discuss the benefits of
`using such as pedal curve and its freeform combination for miniature camera lens optimization. Section 2 briefly
`explains some design challenges of miniature camera lenses. Section 3 shows how we set up a benchmark lens from
`an existing patent. Section 4 explains the use of the pedal curve to the ellipse on miniature camera design. In Section
`5 the evaluation design we optimized is compared with the benchmark lens.
`
`2. Challenges of miniature camera lenses
`
`Lens designers face challenges when designing miniature camera lenses compared to conventional large scale
`camera lenses. The most limiting specification is the package size. In order to avoid color crosstalk on the digital
`sensor, the image space chief ray angle (CRA) is limited, usually no more than 30 degrees [2]. The stop aperture
`must be located close to the first surface to fulfil the CRA requirement, which cause the lens not to be symmetric
`about the stop. The lack of symmetry about the stop makes correcting distortion and lateral color difficult. In order
`to efficiently correct aberrations, aspherical surfaces are used extensively with injection molding of plastic. The
`limited choice on plastic materials also makes correcting axial color challenging. Due to the demand of low-light
`performance of the miniature cameras, larger aperture lenses with lower F/# are desired. More lens elements may be
`needed and this makes it difficult to maintain the total track length (TTL). However, mobile devices are becoming
`thinner at the same time, which causes the lens to protrude over the surface of some mobile devices. The relative
`illumination (RI) is often required to maintain at least 50% at the sensor corners [3]. Nevertheless, there is a tradeoff
`between relative illumination and aberration control during the lens optimization.
`
`3. Benchmark lens
`
`The starting point of our benchmark lens design is from the first embodiment in U.S. Patent 9,110,270. The patent
`lens contains five lens elements with an IR filter in front of the sensor. The lens is re-optimized into our benchmark
`lens using only conventional even aspherical surfaces with the design specifications provided in Table 1. The
`number of aspheric coefficients for each surface remains the same in the patent specification.
`
`Table 1. Design specifications for benchmark lens and evaluation lens
`
`Wavelength
`
`f [mm]
`
`F, d, C
`
`4.1
`
`F/#
`
`2.2
`
`FOV [deg]
`
`TTL [mm]
`
`Distortion
`
`Edge RI
`
`69.8
`
`<5.2
`
`<1%
`
`>50%
`
`4. Evaluation Lens
`
`The rear group of miniature camera lenses usually contains one or two elements that are strongly aspheric to correct
`field curvature, astigmatism and distortion [4]. The shape of these elements cannot be easily explained as the
`aspheres become dominant at large field angles [2]. However, these lens elements often contain surfaces with
`different curvature direction between the center of the surface and the edge (e.g., concave in the center and turning
`
`APPLE V COREPHOTONICS
`IPR2020-00906
`Exhibit 2031
`Page 1
`
`

`

`JTu3A.3.pdf
`
`Design and Fabrication Congress 2017 (IODC,
`Freeform,OFT) © OSA 2017
`
`back to convex before the edge). It is noted that this surface profile can be described by the pedal curve to the
`ellipse. The sag S(r) of this pedal surface is obtained by rotation about z-axis
`
`𝑆(𝑟) = 𝑏 − √𝑏2 − 2𝑟2 + √𝑏4 + 4(𝑎2 − 𝑏2)𝑟2
`2
`
` , (1)
`
`where a is the major axis of the ellipse, b is the minor axis, and r is the radial distance from the optical axis. A
`freeform polynomial surface [1] can be written as
`
`
`
`3(𝑟), (2) 𝑧𝑝(𝑟) = 𝐴1𝑆1(𝑟) + 𝐴2𝑆12(𝑟) + 𝐴3𝑆13(𝑟) + 𝐵1𝑆1(𝑟) + 𝐵2𝑆12(𝑟) + 𝐵3𝑆1
`
`
`
`
`
`
`
`where S1(r) and S2(r) are two sets of pedal surfaces, A1 – A3 and B1-B3 are coefficients. Our design used the
`freeform surface to replace surface 7, surface 9, and 10 of the benchmark lens.
`
`5. Lens comparison
`
`The layouts and the optical path difference (OPD) plots of both benchmark and evaluation lenses are shown in Fig.1.
`The freeform surfaces are marked on the evaluation lens. Most layout differences come from the rear group.
`Package sizes remains the same for both lenses. For the aberration control, OPD are evaluated at over 4 equal-area
`fields. The evaluation lens shows more uniform performance over the field of view, while the OPD performance
`downgrade significantly at larger field of view for the benchmark lens. Such downgrade in performance at large
`field of view can be also observed from the MTF plot in Fig.2. The evaluation lens shows more uniform contrast
`performance over the field.
`
`Fig.1. Lens layout and OPD plots for the benchmark lens (left) and the evaluation lens (right)
`
`
`
`Fig.2. MTF plots for the benchmark lens (left) and the evaluation lens (right), the red brackets show the contrast distribution over the field
`
`
`
`6. Conclusion
`
`We briefly discussed our research about miniature camera lens optimization using surfaces based on the pedal curve
`to the ellipse. Our evaluation lens shows better aberration control at large fields of view and uniform contrast
`distribution at high spatial frequencies. In addition, the number of parameters to describe the pedal surfaces is
`decreased as compared to the benchmark design. Overall, we show that freeform surfaces based on the pedal curve
`to the ellipse might be useful in imaging lens design.
`
`7. References
`
`[1] José Sasián, Dmitry Reshidko, Chia-Ling Li, “Aspheric/freeform optical surface description for controlling illumination from point-like light
`sources,” Opt. Eng. 55(11), 115104 (2016).
`[2] Peter P. Clark, “Mobile platform optical design,” Proc. SPIE 9293, 92931M (2014).
`[3] Jane Bareau , Peter P. Clark, “The optics of miniature digital camera modules,” Proc. SPIE 6342, 63421F (2006).
`[4] Dmitry Reshidko and Jose Sasian, "Optical analysis of miniature lenses with curved imaging surfaces," Appl. Opt. 54, E216-E223 (2015).
`
`APPLE V COREPHOTONICS
`IPR2020-00906
`Exhibit 2031
`Page 2
`
`