When I think about the optical resolution capabilities of a microscope designed for protein drop imaging, I think about the smallest size crystal I could possibly resolve. And in fact, Wikipedia defines optical resolution as “the ability of an imaging system to resolve detail in the object that is being imaged”.
Figure1: 1951 USAF resolution test chart. Source: Wikipedia
No conflict, right? This could be the end of the post, if it wasn’t for one small detail: Protein drops are three dimensional. And an optical resolution is generally measures with two dimensional test patterns. Consider the 1951 USAF resolution test chart in figure 1. A series of horizontal and vertical lines are used to determine the smallest size object – or line separation – that could be resolved by a given optic. In contrast, when a three dimensional object is to be imaged, concessions need to be made between depth of field, DOF, and highest optical resolution at a specific focal plate. The DOF is generally determined by the relative aperture or f-number. Increasing the DOF implies lower overall optical resolution of the image since resolution drops off gradually around the maximum resolution any optic can achieve (again, a good summary is given in Wikipedia). Figure 2 illustrate this behavior: The maximum line pair resolution is only achieved in a single point in the focal plane, increasing the depth of field increases the focal plane, but as a consequence, line pair resolution is reduced for points away from the optimum focal plane.
Figure 2: Line pair resolution as a function of depth of field.
For protein drop imaging, especially in automated fashion, the DOF should be adjusted to match the height of the drop. This way, the content of the drop can be adequately represented by a single image. Otherwise, if the DOF is smaller than the height of the drop, various images need to be taken at different focal planes and either inspected individually, or assembled into a composite image with adequate focus across the drop using a software application. This technique is commonly referred to as “slicing” and comes at a significant cost in terms of imaging acquisition time and CPU requirements.
Figure 3: Slicing, optical resolution and depth of field
Slicing can increase the optical resolution since the depth of field is reduced for each slice, and therefore each image is taken closer at the best line pair resolution level. This technique also mimics how we would use a typical bench top microscope where we would scan through a drop by changing the focal plane. For automated high throughput image acquisition this technique comes at a significant disadvantage, since imaging speed and the sheer amount of imaging data are of major concern.
The correct approach for high throughput imaging is to design optics that match the depth of field of the types of objects we are most likely to image, which would be smaller (sitting) drops and larger (hanging) drops. This approach can only be successful if we pay attention to another optics parameter: The field of view or field of vision (FOV), or the extend of a well in a crystallization we can observe at the time of taking the image. In an interactive scenario this is less relevant since we can move the plate around as part of the investigative process, but in high speed imaging, we better make sure to capture the entire drop. The best way of doing this is by designing optics where DOF and FOV match the dimensions of the objects you are trying to image.
So, how do you measure the optical resolution of your optics at a depth of field that matches our experimental conditions? Actually, there is a simple but elegant solution to this problem, discussed by my colleague Jian Xu during the last ACA. First, it makes sense to measure resolution on objects you are interested in imaging which would be small crystals in protein drops. Second, if you can distribute randomly a large number of these objects throughout the volume of question, i.e. the drop, you will image some of the objects at the maximum line pair resolution limit. In practice, what Jian did was to grow a shower of needles in a drop, snap an image and measure the smallest needle diameter he could find. Figure 4 shows a schematic of this setup.
Figure 4: Schematic of Jian's experimental setup to meassure the optical resolution of our new optics.
