The numerical aperture (NA) of the optical system isDimensionlessTo measure the angle range of light that the system can collect.
In different fields of optics, the precise definition of numerical aperture is slightly different.stayopticsThe numerical aperture describes the size of the lens light collecting cone angle, which determines the light collecting ability and spatial resolution of the lens;stayOptical fiberThe numerical aperture describes the cone angle of light entering and leaving the fiber.
Numerical aperture is the main technical parameter of lens and condenser, which is used to judge the performance of both (especially for objective lens)Positional chromatic aberrationThe numerical aperture of ZEISS is an important symbol of the ability to eliminate position color difference and magnification color difference.The value is marked on the shell of objective lens and condenser lens respectively.
The numerical aperture (NA) is the product of the sine of the refractive index (n) and half of the aperture angle (2 α) of the medium between the lens and the object to be tested.The formula is as follows: NA=n * sin α.Aperture angle, also called "aperture angle", is the angle formed by the object point on the optical axis of the lens and the effective diameter of the lens in front of the objective lens.The larger the aperture angle, the greater the luminous flux entering the lens, which is proportional to the effective diameter of the lens and inversely proportional to the distance of the focus.
It must be pointed out here that in order to give full play to the objective numerical aperture,CondenserThe NA value of should be equal to or slightly greater than the NA value of the objective lens.
The numerical aperture reflects the coupling efficiency between the fiber and the light source.There is an air gap between the light source and the end face of the fiber. Only part of the light incident on the end face of the fiber can enter the fiber, and only part of the light entering the end face of the fiber can be fully reflected and propagated in the fiber.It can be seen from the figure that only the light incident from the air gap to the end face of the fiber with an incidence angle less than q0 can propagate.Q0 is actually a spatial angle, that is, if light is incident on the end face of the fiber from a conical region limited to 2q0, the light can be captured by the fiber.The larger the qo, that is, the smaller the difference between the refractive index of the core and the cladding, the stronger the optical fiber's ability to capture light. The parameter sinqo directly reflects this ability, which we call the numerical aperture NA of the optical fiber[1]。
technical parameter
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Numerical aperture is closely related to other technical parameters, which almost determines and affects other technical parameters.It is proportional to the resolutionMagnificationIs proportional,Depth of focusIt is inversely proportional to the square of the numerical aperture, the NA value increases, and the field width isWorking distanceWill become smaller accordingly.
In laser physics
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staylaserIn physics, the definition of numerical aperture is slightly different.The laser beam diverges at a very small angle during its propagation.Far away from the narrowest point of the beam, the divergence of the beam is roughly linear with the propagation distance - equivalent to the beam forming a cone in the "far field".In this case, the definition of numerical aperture is still:
However, the definition of θ is different from the previous one.The laser beam is not a sharp cone due to the limitation of the aperture, but a Gaussian beam whose irradiance gradually decreases with the distance from the beam center.In view of this situation, laser physicists choose to define θ by the divergence degree of the beam, that is, θ is determined by the propagation direction of the light and the distance from the central axis of the beam when the irradiance is reduced to 1/e of the total irradiance of the wave front.For Gaussian laser beam, its numerical aperture is related to the minimum laser beam spot size (its numerical aperture represents the laser divergence degree, which is related to the minimum laser beam diameter):
Numerical aperture calculation formula
Where λ 0 is the wavelength of the laser in vacuum, and 2w0 is the diameter of the beam spot at the narrowest part of the beam (equivalent to the full width when the irradiance decays to 1/e).This means that the laser focused on a small beam spot will diverge quickly, while the laser with a larger beam spot diameter can maintain its diameter almost unchanged over a long propagation distance.
In fiber optics
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In multimode fiber, only the light entering the fiber along a specific cone angle (the so-called receiving cone angle) can propagate along the fiber.The half angle of the cone angle is called the receiving angle θ max.aboutAbrupt multimode fiber, the size of the receiving angle only depends on the refractive index of the fiber core and external cladding:
Where n1 is the refractive index of the fiber core, and n2 is the refractive index of the cladding.Although higher angle light can also enter the core layer, it cannot occur at the interface between two layerstotal reflectionAnd therefore cannot be propagated through optical fiber[2]。
Increase numerical approach
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In the microscope system, for a given objective lens, the aperture angle has been fixed. If you want to increase its NA value, the only way is to increase the refractive index n value of the medium.Based on this principle, the water immersion system is producedobjective lenseandOil immersion objective。
Since the refractive index n value of the medium is greater than 1, the NA value may be greater than 1.If bromonaphthalene with high refractive index is used as the medium and the refractive index of bromonaphthalene is 1.66, the NA value can be greater than 1.4[3]。
