Beam shaping

All of us know the problem from taking pictures with a camera: when we focus on an object in the foreground, the background becomes blurred. Likewise, if we focus on objects further away, the foreground goes out of focus. This phenomenon is called “depth of focus”, and all optical systems exhibit this effect due to the laws of wave optics that prevent us from being able to confine light waves to a small spot over a long distance of propagation. In microscopes, this problem is much more severe than in everyday photography because of the much stronger focusing power of the microscope objective compared to a camera objective. For this reason, optics researchers are trying to “bend the rules” of wave optics by cleverly shaping beams of light such that they maintain a small spot size over a longer distance. One way to do this is by using a conical lens (also known as an axicon) instead of a normal spherical lens, as shown in the figure below. Instead of a point-like focal spot, one obtains a long line-like focal region which is surrounded by rings of lower intensity. A cross-section through this focal region looks like the famous Bessel function which one encounters frequently in engineering. For this reason, the focused light intensity distribution behind an axicon is also referred to as a “Bessel beam”.

Illustration of the light intensity distributions obtained when focusing a Gaussian beam with a spherical lens (a) and a conical lens (b). The conical lens produces a Bessel-shaped irradiance distribution with the same resolution as the spherical lens, but with a much greater depth of focus.

Illustration of the light intensity distributions obtained when focusing a Gaussian beam with a spherical lens (a) and a conical lens (b). The conical lens produces a Bessel-shaped irradiance distribution with the same resolution as the spherical lens, but with a much greater depth of focus.

In high-resolution optical coherence tomography (OCT) imaging, beam shaping for increasing the depth of focus is desirable because it allows to capture a full axial depth scan at constant resolution, with no need for shifting the focus. Bessel beams generated with axicons have been the most widely studied approach [1], but other shaped beams generated using programmable devices called spatial light modulators (SLMs) have been proposed [2]. At OBEL, we are studying the properties of various non-Gaussian beams that we generate in the lab using a liquid-crystal SLM (see figure below). We have recently shown that not all Bessel beams are created equal. They possess a unique scale factor called the Fresnel number which allows us to precisely design the depth of focus of our imaging system without sacrificing too much imaging sensitivity [3].

(a) A spatial Light Modulator (SLM) in the OBEL optics lab and (b) an image of the characteristic ring pattern of the far field of a Bessel beam generated using this device.

(a) A spatial Light Modulator (SLM) in the OBEL optics lab and (b) an image of the characteristic ring pattern of the far field of a Bessel beam generated using this device.

Wavefront-shaped beams are not just fascinating from a theoretical point of view. They are also fun to play with experimentally. The figure below shows an image of a lemon taken with a Bessel beam in our lab, clearly showing the improved depth of focus compared to a conventional focused Gaussian beam with the same resolution.

OCT images of a lemon showing the increased depth of focus that can be obtained with a Bessel beam compared to a Gaussian beam. (a) Gaussian beam, (b) Bessel beam. The red bars indicate the depth of focus.

OCT images of a lemon showing the increased depth of focus that can be obtained with a Bessel beam compared to a Gaussian beam. (a) Gaussian beam, (b) Bessel beam. The red bars indicate the depth of focus.

Many interesting questions remain open for exploration in the area of beam shaping for OCT. For example, we are investigating experimentally and with numerical simulations how the wavefronts of various shaped beams are distorted when they propagate through a turbid medium such as biological tissue. When these beams are generated using a programmable device such as an SLM, this leads directly to another fascinating question: can we somehow “pre-compensate” for the wavefront distortion such that the beam it focuses sharply deep inside the biological tissue?

1) Key researchers

2) References

[1] R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Optics Letters 31, 2450-2452 (2006).

[2] L. Liu, C. Liu, W. C. Howe, C. J. R. Sheppard, and N. Chen, “Binary-phase spatial filter for real-time swept-source optical coherence microscopy,” Optics Letters 32, 2375-2377 (2007).

[3] Dirk Lorenser, C. Christian. Singe, Andrea Curatolo, and David D. Sampson. “Energy-efficient low-Fresnel-number Bessel beams and their application in optical coherence tomography.” Optics Letters 39, 548-551 (2014).