Lunam’s special features
The analysis of the light momentum change provides a powerful approach to determine the force applied by an optical trap. However, it requires a more stringent design of the detection instrument. To achieve accurate and precise force measurements, the Lunam T-40i was built with the utmost quality in mind, including the latest developments in force detection:
- The entire design is optimized to obtain a correct decomposition of the beam momentum. This is guaranteed by the system fulfilling the Abbe sine condition through its entire numerical aperture.
- The transmittance of the beam is uniform throughout the whole system.
- The sensor has a uniform responsivity across the active area.
- The temperature dependence of the sensor’s response is calibrated.
- The sensor’s effective radius is precisely measured.
With all these improvements, we obtained an accuracy of ~5% in force measurements for samples of different kinds.
Optimum optical design
The detection of the light momentum requires that the light pattern formed at the detector plane corresponds to the Fourier transform of the light distribution at the trapping plane, and this relation must be fulfilled across the entire plane. In order to guarantee this condition, the optical design involved in the capture and projection of the beam onto the sensor must follow the Abbe sine condition, that is, light propagating with the same angle, θ, must end up at the same position on the detector, r, given by the relation r = f·n·sinθ, where f is the focal length of the instrument and n is the refractive index of the suspending medium.
The Lunam sensor has been carefully designed to obtain an extended range of momentum measurement to thus provide the best performance. The aplanatism of the system is guaranteed for the entire collection angle of the immersion optics (NA = 1.4).
Uniform optical transmittance
It has long been known that a light beam passing through an optical lens group is altered by the non-uniform transmittance of the system. This effect, which degrades the quality in image formation, has also an important impact on the measurement of the momentum of the trapping beam. A problem arises in this case: the force calibration factor is not properly defined as it changes from point to point across the detection plane, and, therefore, the value of the calibration can change depending on the trapping conditions, for example, for different numerical apertures of the objective or for different bead sizes with different scattering patterns.
This effect is mainly concentrated on the front lens of the system. The Lunam T-40i sensor has a specific design to minimize this effect and incorporates different modifications to improve transmittance flatness.
Uniform detector response
The sensor responsivity is one of the fundamental parameters of the photodetector in a force detection instrument. It measures the efficiency with which carriers are generated due to incident light. The response may vary across the detector active area, leading to variations in force calibration. The choice of a uniform response detector is a crucial parameter.
In the following figure, we can observe how low cost sensors (detector 1) can induce significant errors due to changes in responsivity as large as 30-40% compared to high-quality detectors such as those used in the Lunam T-40i (detector 2).
The sensor responsivity depends on different parameters (device material, operating wavelength, bias voltage, etc.) that remain fixed, but also upon magnitudes that can change from one experiment to another. The sensor temperature is one of these critical parameters.
For 1064 nm, this variation can reach 1-2%/ºC, which may represent a significant change if the instrument calibration does not include such dependence. This can easily represent a variation of 5% during the same day if it is not taken into account. To compensate for this, the Lunam sensor incorporates continuous measurements of the sensor temperature to adapt the force readings to the operating temperature. Furthermore, as the sensor responsivity depends on the laser wavelength (for example, the variation for 980 nm is less than 0.1%/ºC), the calibration is performed for the required wavelength.
Sensor’s effective radius
The sensor radius is the magnitude that relates the normalized voltage and the position of the laser spot, x, onto the detector active area:
This quantity does not necessarily correspond to the clear aperture of the device and needs therefore to be calibrated for each sensor.
A thorough measurement of this parameter allows a more accurate force calibration of the Lunam.