Does the condenser's NA affect the microscope's resolution?

The condenser's numerical aperture (NA) strongly impacts a microscope's resolution, since the angular range of the light incident on the sample affects the angular range of light transmitted or reflected by the sample. According to a general rule for optimizing resolution, the condenser NA should be as least as large as the objective NA. In other words, the cone of light provided by the condenser should have an angular range that matches or exceeds that accepted by the objective lens. 

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Figure 2: In epi-illumination microscopes, the objective provides the light that illuminates the sample. It also collects the light reflected and scattered from the sample. Due to this, and in contrast to the case illustrated in Figure 1, both the illumination and imaging angles depend only on the objective. 

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Figure 1: In transmitted light microscopes, light from the light source is directed to the sample by the condenser optical system. The objective lens is used to collect the transmitted light. This collected light is then routed to create an image at a camera or eyepiece.

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Figure 3: Cones describe the light incident on a sample point from the condenser (left, gold), the light transmitted through the sample (right, yellow), and the range of light the objective can collect (right, orange). The cones' angles are measured from the optical axis. The angular ranges of the light cones incident on and transmitted by the sample are approximately the same (θ_cd ), since light that is not absorbed or scattered by the sample travels in an approximately straight line. The angular range (θ_obj ) accepted by the objective lens is can be different. The numerical apertures of the condenser (NA_cd ) and objective (NA_obj ) are often used to compare the angular ranges of the transmitted light to the light the objective lens can gather.

Condenser and Objective
In transmitted light microscopy, the condenser collects light from the source and illuminates the sample (Figure 1). The condenser optical system typically includes several optical elements, which can be aligned to provide uniform illumination of the sample plane. The objective lens is located on the opposite side of the sample plane and collects the light that is transmitted through the sample. This light is then routed to create an image at an eyepiece or camera.

Alternately, the microscope can be configured so the objective both illuminates and collects light from the sample (Figure 2). In this case, there is no separate condenser lens system.  

Numerical Aperture
The condenser provides light to the sample plane over a range of different angles (Figure 3). A cone, drawn with its tip at a point on the sample and its base encircling the light from the condenser, can be used to quantify the range of incident angles (θ_cd ). The light transmitted by this point on the sample has approximately the same angular range. A different cone can be used to depict the angular range of light (θ_obj ) the objective lens is capable of gathering.

These angular ranges can be quantified by each lens' numerical aperture (NA),

NA = n sin(θ ),

which depends on the half-angle (θ ) of the cone, as well as the surrounding medium's refractive index (n ). The higher the NA, the wider the cone describing the angular range. This angle is measured from the optical axis.

As an example, when the objective lens has a 0.7 NA with air (n = 1) between the lens and sample, the lens' angle of acceptance is θ = θ_obj = 44.43°. For the system illustrated in Figure 2, the NA of the illumination and the NA of the collected light are the same, since both light paths pass through the objective lens.

Resolution
The resolution (δ ) of the microscope describes its ability to image two closely spaced points as a separable pair, instead of as a single point. A common equation,

used to estimate this minimum separation includes only the wavelength () and the NA of the objective (NA_obj ). While this equation seems to suggest the NA of the condenser (NA_cd ) does not affect resolution, this is not the case. This equation actually assumes that NA_cd ≥ NA_obj .

When NA_cd ≤ NA_obj , a modified version of the equation,

provides a better estimate and illustrates the importance of the condenser's NA to the resolution.