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Polarization

The strict definition of apochromatism is having three wavelengths of light focusing to the same point. This normally requires a third lens element in the objective. The normal configuration is a positive, low-dispersion crown, combined with two high-dispersion flints, one negative and one positive. The lenses can be cemented, air-spaced, or a combination thereof. Oil-spaced triplet lenses are sometimes seen as well, where the air space is filled with an immersion oil. Spaced triplets, like spaced doublets, have more degrees of freedom, allowing better correction of aberrations.

The antenna, radio frequency (RF) section, filtering and intermediate frequency elements are in the front of a GPS receiver. The antenna collects the satellite’s signals and converts the incoming electromagnetic waves into electric currents sensible to the RF section of the receiver. Several antenna designs are possible in GPS, but the satellite’s signal has such a low power density, especially after propagating through the atmosphere, that antenna efficiency is critical. Therefore, GPS antennas must have high sensitivity, also known as high gain. They can be designed to collect only the L1 frequency, L1 and L2, or all signals, including L5. In all cases, they must be Right Hand Circular Polarized, (RHCP), as are the GPS signals broadcast from the satellites.

Circularly polarizedlight

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Elliptical polarization

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The primary aberration in an achromatic refractor is longitudinal chromatic aberration. Lateral color tends not to be an issue. Both coma and off-axis astigmatism are present and can be problematic for wide-field imaging. An air-spaced objective has less coma than a cemented one. Doublet objectives suffer from slight spherochromatism, where spherical aberration is eliminated in green light but there is slight undercorrection in red and a slight overcorrection in blue. Field curvature exists, so wide field photography may be difficult without a corrector lens, although the limiting factor with an achromat is almost always the chromatic aberration. As with most telescopes, distortion is negligible.

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A simple lens focuses different wavelengths of light to different points. Specifically, red light is focused farther from the lens than blue light. This is longitudinal chromatic aberration. If focused for the green light to which the human eye is most sensitive, the red and blue colors will appear out of focus, yielding a blurry image.

Some residual color exists in the wavelengths outside the visual range. This may result in some violet halos with less-than-ideal designs when used for imaging, but visually a true apochromat should show no significant color aberrations. Coma is significantly reduced, in the neighborhood of 3 to 4 times less than a comparable achromat. Field curvature in a triplet is comparable to that in a similar achromat. Field flatteners are usually available to eliminate curvature for photographic applications. Designs like the Petzval eliminate field curvature.

The lower the dispersion of the crown glass, the less the residual chromatic aberration (the difference between green and red/blue focus). Many telescopes now use extra-low dispersion (ED) glasses to minimize chromatic aberration. These are sometimes called apochromatic refractors, but do not adhere to the strict definition of an apochromat as outlined below.

P-polarized light

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Linear polarization

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Author and/or Instructor: Jan Van Sickle, Senior Lecturer, John A. Dutton e-Education Institute, College of Earth and Mineral Sciences, The Pennsylvania State University; V3 Consultants, Lakewood, CO

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Polarization vector

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The two lenses together make up the telescope objective. There are two basic configurations for the objective: cemented and air-spaced. A cemented objective has the same curvature on the inside surfaces of the lenses (the second and third optical surfaces). This eliminates possible degrees of freedom from the design. This type of objective will normally have more coma than an air-spaced objective and is usually only seen on designs with very small apertures and slow focal ratios. An air-spaced objective gives two additional degrees of freedom (another surface curvature and the thickness of the air space), allowing better control of coma.

Alternate designs are possible, such as the Petzval four-element design popularized by TeleVue. This design uses a long-focal-ratio (over f/10), low-dispersion doublet in combination with two elements farther down the optical path which speed up the focal ratio and flatten the field. The high number of degrees of freedom allow this design to be very well corrected, even at speeds as fast as f/5. This makes it an ideal photographic instrument.

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Unpolarized light

Circular polarization antenna

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Polarized waves oscillate in more than one direction. The electrical field vectors of the GPS Signal have a constant magnitude, but their direction rotates so that the electrical field vector of the wave describes a helix in the direction of propagation. Said another way, circularly polarized waves are those where the angle of the electric vector rotates around an imaginary line traveling in the direction of the propagation of the wave. The rotation may be either to the right or left. The GPS signal is a Right-Hand Circularly Polarized (RHCP) wave. You can illustrate it this way. With your right hand, give the thumbs up signal. Now, instead of pointing your thumb up, point it in the direction that the GPS signal is propagating. Your curling fingers show you the direction of the rotation of the field.

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In the usual configuration a positive lens is made of crown glass. This glass has a low dispersion, spreading the colors out to a lesser extent. Then a flint glass element, with a higher dispersion, is used as a negative element. Chosen correctly, this results in the red and blue wavelengths coinciding at the same focus. The green is still slightly different, but the difference is relatively small. (In the diagram above, the lens on the left is the positive crown, the second lens is the negative flint.)

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This section details the optical design and inherent aberrations of refracting telescopes. For a more basic overview of this design please see theRefractors page. For a review of the optical design terms, see the Optical Aberrations and Optical Design sections.

In a triplet, red, green, and blue light is brought to a single focus. This leaves other colors such as violet out of focus, so there is residual color as in an achromat, but the amount is significantly less. The greater number of lens elements also means better correction of other aberrations such as coma and spherochromatism.