Resolution Assessment of a Microscope Based on a Raspberry Pi Camera

Theory of Optics

The resolution can be limited by two independent factors:

• pixel size;

• diffraction effects.

The larger of these determines the actual limitation of the system. In our case we know that the pixel size is 1.4 μm, so we now need to work out the diffraction limit, that is the smallest spot size which can be produced by the lens with the given specs. To calculate this, recall the Rayleigh criterion for a circular aperture: sinθ=1.22 λ/d. Here λ~550nm is the wavelength of light, taking green for the middle of the visible spectrum, d=1.25mm is the diameter of the aperture and θ (small angle) is the angular radius of the spot, that is tanθ=r/L. Here r is the radius of the spot projected at a distance L from the aperture, which in our setup is actually the focal length f of the Raspberry Pi camera lens (and the spot is projected onto the CCD sensor).


From first approximation for a small angle: sinθ=tanθ, so 1.22 λ/d=r/f. Rearranging this equation and plugging in the numbers gives the following diameter of the smallest resolvable spot: 2r=3.8μm. This is almost three times the size of the pixel on the CCD, which imposes the actual limit on the resolution. The pixels of the CCD outresolve the theoretical lens limits.

Final resolution estimate of a microscope based on Raspberry Pi camera: 3.8μm

Compare this with a typical size of a chloroplast: 5-8μm diameter [1]. Our resolution will be just enough to image them, which is exactly what we have managed to do on this picture of Spirogyra cells. Note that these are larger than typical chloroplasts though. To obtain a better resolution, a lens with either larger aperture and/or shorter focal distance can be used, without the need of a better CCD. However, this is a tradeoff in terms of worse aberration and contrast. An improvement to the resolution will however be required in order to image bacteria, for example, which are of the order of 1μm in diameter [2].

[1] Wise, R. and Hoober, J. (2006). The structure and function of plastids. Dordrecht: Springer.
[2] Encyclopedia Britannica, (2015). bacteria :: Diversity of structure of bacteria. [online] [Accessed 30 Jul. 2015].

Inverting the Lens: Why and How

The way a camera works is by focusing an image of a distant large object as a small set of points onto the CCD, which is positioned close to the lens (in its focal plane). Theoretically however, it might as well do the opposite (because light paths are reversible – a well known and intuitive physical principle): that is, inspect the CCD pixels and project their greatly enlarged image onto a distant screen.
The lens has a small aperture (1.25mm) at one end, and a larger one (4mm) offering a wider view angle at the other, which is required for viewing close up objects. This is normally oriented towards the CCD.

So, if we want to image a sample on a microscope slide, we need to:

• position the lens close to the sample – at roughly the focal distance, that is 3.6mm;

• orient the lens with its larger aperture towards the sample;

• position the sensor behind the lens, now at a much larger distance (roughly 2.8cm) – for this we have designed a special camera mount.

Now we have the Raspberry Pi camera working as a microscope!

The problem: how to unscrew the lens from the camera The Raspberry Pi camera is sold with the lens screwed (and lightly glued) into the sensor casing. To unscrew the lens, you will need the right type of pliers: ideally with ridged surface. Grip the top part of the plastic casing of the lens firmly, being careful not to crush it, and rotate counterclockwise. After the first small rotation, you should be able to unscrew it fully manually. ATTENTION: might not work from the first time! Do not try to cut out the lens or force it out in any other way.

Power Consumption Assessment

OpenScope Power Consumption

Below is a table of the components of our microscope (equivalent for fluorescence and brightfield modes). A typical 8hr day is used for comparison, and the data for the 3D printer is also included for completeness. However, this will of course only be used during assembly and is not included in the running consumption.

Component	Power per unit / W	kWh/day for 8hr use
Raspberry Pi Model B [1]	4.0 *	0.032
20mA LEDs x5 [2]	0.10 **	0.004
Servo Motors x2	7.0 **	0.11
22" LCD Monitor	30 **	0.24
Arduino Uno [3]	0.25 ***	0.004
TOTAL		0.39
3D Printer (Ultimaker 2) [4]	220 **	1.8

* Based on 900MHz quad-core ARM Cortex-A7 CPU
** Numerous models with different characteristics. Values given represent the appliances we’ve used
*** Based on ATmega328 processor

Commercial Microscope Consumption

This data is provided for comparison:

Component	Power per unit, W	kWh/day for 8hr use
HBO 100 Mercury lamp [5]	100 *	0.80
Tungsten-Halogen lamp [5]	100 *	0.80
XBO 75 Xenon arc lamp [5]	75 *	0.60

* Most commonly used lamp wattages according to ZEISS Microscopy Online Campus

Note: Relevant equations for power consumption estimates and unit conversion (Recall your high school physics!)

• Conversion from W to kWh/day for 8 hour use: E_(kWh/day)=P_(W)×t_(h/day)/1000_(W/kW)

• Conversion to W from A (based on 5V DC standard power supply from USB port): P_(W)=I_(A)×U_(V)

[1] Raspberry Pi, (2015). Raspberry Pi 2 Model B. [online] [Accessed 30 Jul. 2015].
[2] RS Components UK, (2015). Lighting | RS Components. [online] [Accessed 31 Jul. 2015].
[3] Arduino.cc, (2015). Arduino - ArduinoBoardUno. [online] [Accessed 30 Jul. 2015].
[4] Ultimaker.com, (2015). Ultimaker 2 | Ultimaker. [online] [Accessed 30 Jul. 2015].
[5] Zeiss-campus.magnet.fsu.edu, (2015). ZEISS Microscopy Online Campus [online] [Accessed 30 Jul. 2015].

Stage Drift Characterisation

In order to perform time-lapse imaging, the digital microscope must be left capturing images for long periods of time. However, most microscope stages exhibit 'drift', which causes the sample to move during the experiment. This can seriously affect the results, and must be fully characterised before solutions are developed. The causes of drift are complex, and can be as a result of thermal expansion, mechanical movement and vibrations amongst other factors [1][2].

In order to characterise our prototype brightfield microscope, an experiment was set up to record the movement of points (fiducial mark) on a slide over a period of roughly 16 hours. This is an established technique for measuring drift [3]. A free, open-source video analysis and modelling software was used to manually track the points over time. Two key conditions were tested: the first was the normal working set-up, the second was carried out with the screws linking the translation knobs to the stage itself removed. This essentially uncouples the stage from the translation knobs, and the sample is then moved until it's in the correct orientation. The experimental objective was to characterise the movements of our 3D printed stage in isolation, and compare this to it's movements when coupled to the translation knobs as it would be when fully functional.

Brightfield Microscope Test 1 (BT1)

Time lapse set-up:

Raspberry pi camera set up to take images at 5 min intervals overnight

Used prototype brightfield microscope, with a standard micrometer slide (one major division = 100µm)

Code used is summarised here and is based on a standard Raspberry Pi camera tutorial

Movie creation and tracking:

Used iMovie to compile still images into a single movie. In total it comprised of 203 images, taken every 5 minutes, displayed for 0.4s each

A single point was tracked using Tracker software carried out over intervals of 20 frames across the entire time lapse

Calibration was achieved using the micrometer scale

Below is the output of the Tracker software for a single trial:

Figure 2: A single point on the slide was tracked at intervals of 20 frames for the entire length of the time lapse (60,600s). Time (s) is plotted on the horizontal, with distance from origin (µm) along x-axis or y-axis plotted on the vertical axis

Figure 3: Distance from origin (µm) along x-axis is plotted on the horizontal, and distance from origin (µm) along y-axis is plotted on the vertical. Graph shows path of the point in 2D space over the course of the experiment

The data for 4 trials were then aggregated to give the following:

Figure 4: Graphs shows aggregated data from 4 trials in BT1. In all trials, the axis and calibration scale were consistent. Error bars indicate ± 1 SD

Brightfield Microscope Test 2 (BT2)

Time lapse set-up:

Raspberry pi camera set up to take images at 5 min intervals overnight

Used prototype brightfield microscope, with a standard micrometer slide (one major division = 100µm)

In order to test the effect of our translation system on drift, the screws connecting the stage to the translation knobs were removed

This was intended to test the mechanical effect of the attached screws on drift

Code used is summarised here

Movie creation and tracking:

Used iMovie to compile still images into a single movie

201 images, taken every 5 minutes, displayed for 0.4s each

A single point was tracked using Tracker software

Tracking was carried out over intervals of 20 frames across the entire time lapse

Calibration was achieved using the micrometer scale

Note that the point tracked in BT2 was not the same as that tracked in BT1

Results from Brightfield Test 2 (BT2):

Image tracking was repeated 4 times, and each time the x and y coordinates were recorded. This was an attempt to reduce the significance of human error in image tracking

The data were combined, and the averaged plotted with error bars indicating ± 1 SD

Note: tracking involves selecting the target point manually through the course of the time-lapse, which will introduce human error

The data for 4 trials were then aggregated to give the following:

Figure 5: Graph shows aggregated data from 4 trials in BT2. In all trials, the axis and calibration scale were consistent. Error bars indicate ± 1 SD

Figure 6: Graph shows aggregated data from 4 trials in BT1 and in BT2 normalised of the same start point. Assumes points experience the same drift anywhere on the slide. In both trial groups, the axis and calibration scale were identical. They were not identical between BT1 and BT2. Error bars indicate ± 1 SD

Conclusions:

Results indicate that the attachment of the screws significantly reduces microscope drift compared to the stage with screws unattached

Results from BT2 suggest from the dynamics of the drift that the stage gradually approaches a stable equilibrium position

One potential solution may therefore be to determine the time taken to reach the equilibrium, and to image only once this has occurred

This will require further experimentation to determine whether the stage does actually reach a stable equilibrium, and how long this takes

However, with a fully motorised stage the screws must be attached, which changes the dynamics of the drift dramatically

Solutions have been proposed that make use of software to counteract drift using autofocus (for drift along z-axis). Additionally piezoelectric stages and automated stepper motors to actively remove drift (for movement along x-axis and y-axis) have also been implemented [3] [4]

In current fluorescent systems artificially labelled beads can be used as fiducial marks in the sample plane. Using a closed-loop feedback system, stage drift can then be corrected for based on the position of the fiduciary mark relative to the camera sensor [2]

Further testing, under different conditions such as different temperatures, will allow determination of the cause of drift when the screws are attached. However this is likely to be due to a number of factors each making a small contribution to overall stage movement.

[1] Microscopyu.com, (2015). Nikon MicroscopyU | Live-Cell Imaging | Focus Drift Correction. [online] [Accessed 10 Aug. 2015].
[2] Microscopedrift.com, (2015). Microscope Drift | The Solution to Focus Drift and Sample Drift. [online] [Accessed 10 Aug. 2015].
[3] Carter, A., King, G., Ulrich, T., Halsey, W., Alchenberger, D. and Perkins, T. (2007). Stabilization of an optical microscope to 0.1 nm in three dimensions. Appl. Opt., 46(3), p.421.
[4] Kreft, M., Stenovec, M. and Zorec, R. (2005). Focus-Drift Correction in Time-Lapse Confocal Imaging. Annals of the New York Academy of Sciences, 1048(1), pp.321-330.

Fact File