Quick Guide to Precision Measuring Instruments
Microscopes
■ Numerical Aperture (NA) The NA figure is important because it indicates the resolving power of an objective lens. The larger the NA value the finer the detail that can be seen. A lens with a larger NA also collects more light and will normally provide a brighter image with a narrower depth of focus than one with a smaller NA value. NA = n·Sin θ The formula above shows that NA depends on N, the refractive index of the medium that exists between the front of an objective and the specimen (for air, n=1.0), and angle θ , which is the half-angle of the maximum cone of light that can enter the lens. ■ Resolving Power (R) The minimum detectable distance between two image points, representing the limit of resolution. Resolving power (R) is determined by numerical aperture (NA) and wavelength ( λ ) of the illumination. R = l (µm) 2·NA l = 0.55μm is often used as the reference wavelength ■ Working Distance (W.D.) The distance between the front end of a microscope objective and the surface of the workpiece at which the sharpest focusing is obtained. ■ Parfocal Distance The distance between the mounting position of a microscope objective and the surface of the workpiece at which the sharpest focusing is obtained. Objective lenses mounted together in the same turret should have the same parfocal distance so that when another objective is brought into use the amount of refocusing needed is minimal.
■ Finite Optical System An optical system that uses an objective to form the intermediate image at a finite position. Light from the workpiece passing through the objective is directed toward the intermediate image plane (located at the front focal plane of the eyepiece) and converges in that plane.
Objective lens
Light from point source is focused at the intermediate image plane
A point-source on the workpiece
Magnification of the objective = L 2 /L 1
L 2
L 1
■ Focal Length (f) unit: mm The distance from the principal point to the focal point of a lens: if f1 represents the focal length of an objective and f2 represents the focal length of an image forming (tube) lens then magnification is determined by the ratio between the two. (In the case of the infinity-correction optical system.) Objective magnification = Focal length of the image-forming (tube) lens Focal length of the objective
200 200
200
Example: 1X =
Example: 10X =
20
■ Focal Point Light rays traveling parallel to the optical axis of a converging lens system and passing through that system will converge (or focus) to a point on the axis known as the rear focal point or image focal point. unit: mm Also known as depth of field, this is the distance (measured in the direction of the optical axis) between the two planes which define the limits of acceptable image sharpness when the microscope is focused on an object. As the numerical aperture (NA) increases, the depth of focus becomes shallower, as shown by the expression below: DOF = l l = 0.55μm is often used as the reference wavelength 2·(NA) 2 Example: For an M Plan Apo 100X lens ( NA = 0.7 ) The depth of focus of this objective is 0.55μm = 0.6μm 2 x 0.7 2 ■ Depth of Focus (DOF)
Working distance
Parfocal distance
■ Infinity Optical System An optical system where the objective forms its image at infinity and a tube lens is placed within the body tube between the objective and the eyepiece to produce the intermediate image. After passing through the objective, the light effectively travels parallel to the optical axis to the tube lens through what is termed the infinity space within which auxil- iary components can be placed, such as differential interference contrast (DIC) prisms, polarizers, etc., with minimal effect on focus and aberration corrections.
■ Bright-field Illumination and Dark-field Illumination
In brightfield illumination a full cone of light is focused by the objective on the specimen surface. This is the normal mode of viewing with an optical microscope. With darkfield illumination, the inner area of the light cone is blocked so that the surface is only illuminated by light from an oblique angle. Darkfield illumination is good for detecting surface scratches and contamination. ■ Apochromat and Achromat Objectives An apochromat objective is a lens corrected for chromatic aberration (color blur) in three colors (red, blue, yellow). An achromat objective is a lens corrected for chromatic aberration in two colors (red, blue).
Objective lens
Image forming (tube) lens
A point-source on the specimen
Light from point source is focused at the intermediate image plane
Magnification of the objective = f 2 /f 1
f 1
f 2
Infinity space
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