Miniature cameras for consumer electronics and mobile phones are a rapidly growing technology. The photographic performance of these tiny, always ready-for-action lenses is remarkable, as it rivals that of single-lens reflex cameras. However, the system level requirements—such as manufacturing cost, packaging, and sensor characteristics—impose unique challenges for optical designers. Beyond adding more optical elements, developers have explored other manufacturing technologies and lens design solutions to expand the imaging capabilities of miniature camera lenses.
A curved image sensor can potentially improve the chief ray incidence angle (CRA) on the sensor, as well as the aberration balancing, image quality, packaging, and manufacturing tolerance sensitivity. It enables the design of simpler, more compact, and lower-cost optics.1–3 In this article we summarize our research using these curved surfaces to design compact miniature lenses for mobile applications.4
Digital image sensors become less efficient when the incident light is at higher obliquity. The field of view (FOV) of the mobile camera is large, and the CRA proportional to the FOV.5–7 Therefore, for better CRA control, the aperture stop in a conventional mobile lens is placed close to the front, away from the image plane. However, if the image sensor is curved, the CRA is significantly reduced. Thus, the stop location has more flexibility and can be moved to make the lens system less unsymmetrical about the stop. Moreover, decreased incidence angles on the sensor reduce crosstalk between adjacent pixels. Figure 1 shows optical layouts of a typical flat field mobile lens and a representative design imaging on a curved surface.
Optical layout of a mobile camera. (a) Conventional flat field design based on existing patent.8
(b) Representative lens imaging on a curved sensor. The chief ray incidence angles on the curved image sensor are significantly reduced. FOV: Field of view. f: f-number.
The power distribution in the lens imaging on a curved sensor is more symmetrical about the stop. In a symmetrical or nearly symmetrical optical system, all odd aberrations tend to cancel out, permitting a higher level of aberration correction. Figure 2 shows a normalized power distribution per optical element for both lenses. The plot provides an indication of where the optical power originates within the system.
Figure 2. Normalized weighted power per optical element for a flat field design and a representative lens imaging on a curved sensor. A curved image surface allows more symmetrical power distribution around the aperture stop.
In a flat field lens, we obtain field curvature correction by introducing negative optical power, and this leads to more overall optical power. Field curvature correction optically stresses a lens, and aberration residuals grow larger.9 For a given image quality, a lens with a curved imaging surface can have faster optical speed due to reduced optical stress. Field curvature aberration is compensated by the curved sensor.
Figure 3 shows the modulation transfer function (MTF) for both lenses. The lens designed for a curved image sensor is not only one f-number faster compared with the conventional design, but also shows more uniform MTF over the field. It would be very unlikely to achieve similar aberration correction for this f-number for a flat sensor with five lens elements.
Figure 3. Modulation transfer function (MTF) of a mobile camera. (a) Conventional flat field design at f/2.2. (b) Representative lens imaging on a curved sensor at f/1.6. The lens imaging on a curved sensor is one f-number faster and shows more uniform performance over the field. OTF: Optical transfer function.
The total length of a mobile camera is an important design parameter. A shorter lens, such as a telephoto lens, imposes optical stress on the system, and departs more from the symmetry by introducing more optical power in the individual elements. As the aberrations substantially increase with lens stress, it would be nearly impossible to control the remaining aberrations for the required FOV and focal ratio (f/#). Thus, in practice, we obtain no substantial reduction in length using a curved image sensor.
Tilts and decentering have the greatest effect on the performance of the mobile lens. We may evaluate the effect of misalignments for a lens element decenter of 5μm and tilt of 0.1deg. However, in practice much tighter tolerances are specified to increase lens manufacturing yield.10–12
Since the tolerance sensitivity strongly depends on the focal ratio of the lens, we compared both flat field and curved sensor designs at f/2.2. We also evaluated the tolerance sensitivity of the representative lens imaging on a curved sensor at f/1.6 (see Figure 4). As expected, the f/1.6 lens is the most tolerance-sensitive, and manufacturability may be a limiting factor for this design. Comparison of lenses at f/2.2 showed that the lens imaging on a curved sensor performed better under manufacturing tolerances than a conventional design.
Figure 4. Sensitivity to lens element decenter (left) and tilt (right). Lens imaging on a curved sensor shows better as-built performance. The horizontal line indicates the nominal criterion value. RSS RMS: Root sum square, root mean square.
In summary, the curved image surface enables a design with equivalent performance but a faster focal ratio than the conventional design. We achieved about one f-number improvement in speed, while preserving uniform image quality over the entire FOV. Small f-number lenses provide better quality and low-light imaging, and can accommodate a larger number of sensor pixels, leading to better resolution. The aperture stop location between the first and second elements is optimal for aberration balancing and controlling the total length of the system. We believe that in practice, a curved image surface will not allow substantial reduction in the length of a mobile camera.
The radius of curvature of the sensor in our design is about 11mm for a 4.5mm focal length lens. Although we are unaware of any commercially available curved sensors suitable for mobile applications, there have been recent reports of significant progress toward their development.13–18Our future research on miniature camera lenses will involve optimal tolerance analysis, polarization aberrations, stray light analysis, and methods for rapid lens evaluation and optimization.
Dmitry Reshidko, José Sasian
College of Optical Sciences
University of Arizona
Dmitry Reshidko is a PhD candidate whose research involves development of novel imaging techniques and methods for image aberration correction, innovative optical design, fabrication, and testing of state-of-the art optical systems.
José Sasian is a professor whose interests are in optical design, illumination optics, teaching optical sciences, optical fabrication and testing, telescope technology, opto-mechanics, lens design, light in gemstones, optics in art and art in optics, and light propagation. He is a fellow of SPIE and the Optical Society of America, and is a lifetime member of the Optical Society of India.
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