Holografische Pinzette

Principle of Operation Movement and Rotation Aberration Correction Twin Traps

It is well known that light transports energy. But photons, the quanta of light, additionally carry  momentum. By using this momentum of light it becomes possible to move small particles like viruses, cells, or micromechanical objects. Light, which interacts with an object generally is deflected. In the ray-optical model this deflection is described by reflection and refraction. Deflection of the photons leads to a change in momentum for the photons since the heading of the photons change. Due to the momentum conservation principle there has to be an opposed change in momentum of the object that interacted with the photons. Change in momentum (per time) leads to force. For every incident ray onto an object we, therefore, can compute the force acting on the object. An integration of all rays focused onto a transparent object (e.g. a glass sphere) leads to a resulting force that pushes the object towards the focus of the light field.

In a conventional optical trap one focused spot is controlled by mirrors or accusto-optical deflectors in order to move objects. Holographic optical tweezers (HOT) however use another approach for generating the trapping field. Fig. 1 shows the principle setup which is based on a conventional microscope consisting of a microscope objective, a tube lens and a camera.

The laser that is used for trapping is coupled into the microscope objective by a beam splitter and a telescope. We now introduce a spatial light modulator (SLM), typically a high resolution liquid crystal display (LCD), into a plane conjugate to the pupil of the microscope objective. The light field directly behind the SLM, therefore is Fourier transformed by the microscope objective. In other words: The intensity distribution in the object plane corresponds to the intensity of the Fourier transform of the hologram displayed by the SLM. By changing the hologram the light field in the object plane is changed instantaneously.

In order to compute the holograms in video-realtime we preferably use the graphics processing unit (GPU) of consumer graphics boards that are normally used for gaming.

Compared to conventional tweezers we have the following properties for a HOT system:

• No mechanical moving parts
• Highly accurate 3D control of the traps (below 5 nm)
• Trapping potentials optimized for specific specimen
• Independent movement and rotation of several objects in 3D simultaneously (see below)
• Possibility to correct for aberrations (see below)
• Reduced light efficiency
• Increased computational load
• Possibility to trap at reduced numerical apertures (see below)

Movement of the trapped objects is achieved by moving the reconstructed spot via a change of the hologram. For lateral movement a phase wedge is added to the hologram. Axial movement is obtained by adding a quadratic phase term to the hologram. More sophisticated computation of the holograms is possible by using optimizing hologram algorithms.

Rotation of micro-objects by light can be realized by direct transfer of angular momentum but for large particles (diameter above 2 microns) we prefer a multispot technique as shown in Fig. 2. Here, two (or more) spots are used for trapping one object (in Fig. ??? a yeast cell). By controlling the relative position of the traps one can rotate non-symmetric objects in a controlled way.

Typically, wavelengths in the near-infrared region are used for trapping because the potential harm to the specimen due to the strongly focused radiation is minimum in this spectral region. With HOT it is anyway possible to reduce the concentration of light - and therefore potential harm - for large particles like cells, by homogeneously illuminating the whole object.  Sometimes, on the other hand, one wants to destroy or cut objects. In this case operation is best performed in the ultraviolet spectral region, as light in this region is absorbed by biological materials. Here, unfortunately liquid crystal- based SLMs are no option and micromechanical-based modulators have to be used, like i.e. the  Digital Micromirror Device by Texas Instruments.

 

The imaging of biological specimen often is degraded by aberrations due to the specimen itself. Most noticeable are spherical aberrations due to a refractive index mismatch. Of course such aberrations that reduce the resolution of optical imaging also might lead to problems for optical trapping. This is directly obvious when trapping of small (in the range of 1 lambda) objects is required. 

Compared to conventional traps the HOT can easily correct such aberrations. To this end one just has to incorporate the phase-conjugate of the aberration into the hologram. Different methods have been implemented in the past to first measure the aberrations and then correct them with the SLM. By this approach the Strehl ratio of the generated light field - and therefore the trapping efficiency - increases.

Fig. 4: a) aberrated trap, b.) corrected trap (images were taken at the same exposure time)	Fig. 5: corrected (top) and uncorrected (bottom) images of spherical beads obtained with the imaging system of a HOT system

Three-dimensional optical trapping with a single optical system normally is only possible for high numerical aperture (NA) because with medium or low NA there is strong forward scattering force that pushes the object out of the trap. Typically,  immersion at numerical apertures above 1.0 are used. Such high NA systems unfortunately lead to a small working distance and a small depth of focus.

The holographic approach allows one to overcome these limitations by the so-called "Twin Trap" approach. Here, we use simultaneously two traps to trap one object. The two traps are located at different axial positions (see Fig. 6). The lower trap is reflected at the (dichroit) object plate. Therefore two counterpropagating beams are generated, which are brought to focus in the same position in the object volume. By this approach, the forward scattering forces of the two traps, which normally pushes the objects out of the traps, cancel each other and stable 3D-trapping is achieved.

Fig. 6:Principle of the twin trap: two axially separated traps are holographically generated. The focus of the second trap lies — after reflection at the object slide — at the focus of the first trap. (images were taken at the same exposure time)	Fig. 7: Stable axial trapping with a twin trap (a). By turning off the reflected trap, the bead is pushed out of the focus (b) towards the reflecting object slide (c), shown here by defocusing the microscope.