Microscope "Numerical Aperture (NA)": A More Important Parameter Than Magnification
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I. What Is NA? Definition and Principle
1. Core Definition
NA is an indicator measuring the light-gathering ability and resolution of an objective lens, representing "the ability to capture light" — a higher NA means more light collected and clearer imaging (e.g., an NA of 1.4 collects approximately 3 times more light than an NA of 0.8, making it superior for observing weak signals).
2. Calculation Formula and Key Conclusions
Formula: NA = n × sinθ (where n = refractive index of the medium, θ = half-angle of aperture, with a maximum of 90°, and sin90° = 1)
- Conclusion 1: The higher the medium’s refractive index (n), the higher the upper limit of NA. For example, air (n=1.0) has an NA upper limit of 1.0; oil immersion (n=1.515) has an upper limit of 1.515 — this explains why oil-immersion objectives can have an NA higher than 1.0 and are the first choice for high-resolution observation.
- Conclusion 2: The larger the half-angle of aperture (θ, i.e., the wider the objective opening), the higher the NA. High-end objectives expand θ through optimized optical design (e.g., increasing the number of lenses, using special glass materials) to improve NA.
3. Direct Correlation with Resolution
According to Abbe’s Resolution Formula (proposed by Ernst Abbe in 1873), a microscope’s resolution (d, the minimum distance between two distinguishable adjacent objects) is inversely proportional to NA:
d = 0.61 × λ / NA
(where λ = wavelength of the light source, e.g., the average wavelength of visible light λ=550nm).
This means: With a fixed light source wavelength, a higher NA results in a smaller resolution d, allowing observation of finer details. For example:
- When observing with visible light (λ=550nm), an objective with NA=0.8 has a resolution d=0.61×550nm /0.8≈421nm;
- Under the same wavelength, an objective with NA=1.4 has a resolution d=0.61×550nm /1.4≈240nm;
- With oil-immersion medium (n=1.515) and NA=1.5, the resolution can be further improved to d≈0.61×550nm /1.5≈223nm.
It is evident that doubling the NA (from 0.7 to 1.4) can approximately double the resolution — an effect impossible to achieve by simply increasing magnification. This is the core scientific basis for why NA is more important than magnification.
II. Three Core Impacts of NA: Resolution, Image Brightness, and Depth of Field
Numerical aperture not only determines resolution but also directly affects image brightness and depth of field (the thickness range of a sample that can be clearly imaged). Together, these three factors determine the practical performance of a microscope.
1. Impact 1: Resolution (Most Critical)
As shown in Abbe’s formula, NA is the "determinant" of resolution. High-NA objectives can distinguish details that low-NA objectives cannot:
- A 40× objective with NA=0.8 (d≈421nm): Can clearly show the morphology of E. coli (0.5-1μm) but cannot resolve surface flagella (≈20nm in diameter);
- A 100× oil-immersion objective with NA=1.4 (d≈240nm): Can observe the distribution of flagella; observing 20nm nanoparticles requires an objective with higher NA and a special light source.
2. Impact 2: Image Brightness
Image brightness is proportional to the square of NA (brightness ∝ NA²) — doubling the NA quadruples the brightness. This is critical for observing weak signals (e.g., fluorescently labeled low-expression proteins, transparent biological samples):
- A European hospital used an objective with NA=0.75 to observe fluorescent cells. Insufficient brightness required prolonged exposure, reducing cell viability;
- After switching to an objective with NA=1.4, brightness increased by approximately 3.5 times, shortening exposure time and preserving cell viability.
3. Impact 3: Depth of Field (DOF)
NA is inversely proportional to depth of field — a higher NA results in a smaller DOF:
- High NA (1.4): Suitable for thin samples or surface details (e.g., chip solder joints); frequent focus adjustment is required for thick samples;
- Low NA (0.3): Suitable for thick samples (e.g., ores); can observe multiple layers at once but has lower resolution.
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