Normally magnifiers are expressed in terms of the magnifying power when \(L=\infty\) (case 3 above). For example, a magnifier with a power of 10 Diopter has a MP equal to \(2.5\) or \(2.5 \times\). In other words, the image is \(2.5\) times larger than it would be if the object would be at the near point of the unaided eye.

Modulation transferfunctionimage processing

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Modulation transferfunctionRadiology

3.6: Magnifying Glasses is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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In practice \(d_{0} \mathfrak{D}=d_{o} /\left|f_{o}\right|\) is much larger than 1 , so that MP is similar in the three cases.

As an example, a diffraction-limited lens with an f/# of 4 and a working wavelength of 0.55µm, the cut-off spatial frequency is approximately 454lp/mm and the MTF is approximately 0.50 at the spatial frequency of 1837 lp/mm. • Manufacturing tolerances An optical system cannot perform better than its diffraction-limited MTF. Manufacturing errors and internal-reflections of optical systems can decrease the MTF values. Typical manufacturing tolerances are listed in the following table.

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Modulation transferfunctionin Ophthalmology

Mtf functionformula

\[\left.\operatorname{MP}\right|_{L=\infty}=d_{0} \mathfrak{D}, \nonumber \] for every distance \(l\) between the eye and the magnifying glass. The rays are parallel, so that the eye views the object in a relaxed way. This is the most common use of the magnifier.

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Modulation transferfunctionformula

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MTFOptics

1.4.3 Contrast (Minimum): The visual presentation of text and images of text has a contrast ratio of at least 4.5:1, except for the following: (Level AA).

The kinematic coupling constraints are useful in cases where a large number of nodes (the coupling nodes) are constrained to the rigid body motion of a single ...

Knowing the possible MTF curves and manufacturing tolerances can help optical designers more accurately predict the system performance and estimate fabrication costs of optical products.

Linear Magnification - In the case of the apochromatic objective in Figure 1, the linear magnification is 60x, although the manufacturers produce objectives ...

The magnifying power MP or angular magnification \(M_{a}\) is defined as the ratio of the size of the retinal image obtained with the instrument and the size of the retinal image as seen by the unaided eye at normal viewing distance \(d_{o}\). To estimate the size of the retinal image, we compare in both cases where the chief ray through the top of the object and the centre of the pupil of the eye hits the retina. Since the distance between the eye lens and the retina is fixed, the ratio of the image size on the retina for the eye with and without magnifying glass is: \[\mathrm{MP}=\frac{\alpha_{a}}{\alpha_{u}}, \nonumber \] where \(\alpha_{a}\) and \(\alpha_{u}\) are the angles between the optical axis and the chief rays for the aided and the unaided eye, respectively, as shown in Figure \(\PageIndex{2}\). Working with these angles instead of distances is in particular useful when the virtual image of the magnifying glass is at infinity. Using \(\alpha_{a} \approx y_{i} / L\) and \(\alpha_{u} \approx y_{0} / d_{0}\) with \(y_{i}\) and \(y_{0}\) positive and \(L\) the positive distance from the image to the eye (with as requirement : \(L \geq d_{o}\) ), we find \[\mathrm{MP}=\frac{y_{i} d_{0}}{y_{0} L} . \nonumber \] Since \(s_{i}<0\) and \(f_{o}<0\) we have, \[\frac{y_{i}}{y_{o}}=\frac{s_{i}}{s_{o}}=1+\frac{s_{i}}{f_{o}}, \nonumber \] where we used the lens equation for the magnifying glass. We have \(s_{i}=-\left|s_{i}\right|=-(L-\ell)\), where \(C\) is the distance between the magnifying glass and the eye. Hence, \(( \(\PageIndex{2}\) )\) becomes: \[\begin{aligned} \mathrm{MP} &=\frac{d_{0}}{L}\left[1+\frac{L-\iota}{\left|f_{o}\right|}\right] \\ &=\frac{d_{0}}{L}[1+\mathfrak{D}(L-\iota)], \end{aligned} \nonumber \] where \(\mathfrak{D}\) is the power of the magnifying glass.

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MTFimage quality

Mtf functionin optical

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Optical design is the process of studying application requirements and designing optical systems to meet specific needs of optical instruments. The entire system may include optics, light source, sensor, electronics boards, display device, and/or other components. The system performance is not totally dependent on the optics. Every component within the system has contributions to the overall performance of optical instruments. For creating optical specifications and designing the optical components or assemblies, designers need to have a wide knowledge of opto-electronic components such as optical receivers and light sources, know the system performance limits, in-depth understand manufacturing tolerances and fabrication costs.

Where λ is the wavelength expressed in mm and f/# is the lens focal-ratio. An optical system cannot transmit information of spatial frequencies higher than the cutoff frequency. The diffraction-limited MTF is used to predict the upper performance limit of a lens system.

The lens formula is 1/f = 1/Do + 1/Di where f is the focal length of the lens, Do is the distance from the object to the lens and Di is the distance of the ...

A magnifying glass causes an image on the retina which is larger than without the magnifier. In principle, the image on the retina can be increased by simply bringing the object closer to the eye (reduce \(\left|s_{o}\right|\) at fixed \(s_{i}\) ). But \(\left|s_{o}\right|\) can not be smaller than the near point \(d_{o}\), which we take here to be \(25 \mathrm{~cm}\). It is desirable to use a lens that makes a magnified erect image at a distance to the eye greater than \(d_{o}\). This can be achieved by a positive lens with the object closer to the lens than the first focal point, thereby producing a magnified virtual image. An example is given in Figure \(\PageIndex{1}\).

3. The object is at the focal point of the magnifier \(\left(s_{0}=f_{o}\right)\), so that the virtual image is at infinity \((L=\infty)\) and hence

The Modulation Transfer Function (MTF) is an important tool to quantify the overall imaging performance of a system. MTF is a function of spatial frequency (v), which is generally in the form of line pairs per millimeter (lp/mm). Every component within the system has an associated modulation transfer function. This includes the imaging lens, sensor, electronic board, etc.

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