I am writing this article after reading some conflicting and confusing information about camera lenses and how they work. One discrepancy was the statement that the act of focusing on a close up subject would change the focal length. That just did not sit right because the zoom ring is what is supposed to change the focal length. Another active discussion revolves around whether or not for a given lens the digital sensor size affects magnification the same as a 35mm film plane. My instinct says it doesn’t, but there seemed to be plenty of credible sources that say it does. The more I researched the more new questions I encountered. My basic premise was (and is) that the laws of physics are immutable, but underlying assumptions can affect our understanding of these laws. So, my quest was to research the basic math that describes lens behavior.
The objective of this article is to consolidate the information I researched and to attempt to better explain some of the conflicting terminology.
We will start with the fact that a camera lens is really not a simple lens in optical terms. A true "lens" is a single piece of glass (or other transparent material) having one or more curved surfaces that alter the convergence of light rays. Some common basic lens shapes are shown below.
A camera lens is composed of multiple lens elements assembled and fitted together in a tube called a lens barrel. This photographic lens is known as an "objective" or compound lens. The term objective refers to the complete optical system. Sometimes it is also used to identify the lens element that is closest to the subject. The camera lens receives light rays from an object and projects them on an image plane. So, it should also be thought of as a projection system.
A camera lens may be designated as prime or zoom. A prime lens has a fixed focal length that does not change. A zoom lens is one that allows the user to alter the focal length. Prime lenses are generally higher quality while zoom lenses offer more flexibility.
These lenses may also be designated as normal, wide-angle, or telephoto. A normal lens renders front to back spacing between objects such that depth perception appears to be the same as that observed by the unaided human eye. Depth perception is where parallel lines converge in the distance and near objects appear larger than distant objects. Wide-angle lenses have less magnification than a normal lens but they have a greater field of view. They can distort depth perception, by expanding the apparent distance between objects. Conversely, telephoto lenses have more magnification than a normal lens but with a smaller field of view. They also can distort depth perception, this time by compressing the apparent distance between objects. A normal lens may not be your favorite. That will depend more on your taste and shooting styles; portraits, landscapes, close-ups, wildlife, and other.
The perceptions of the eye and the camera lens may be similar, but they are not equal. The eye and brain see two images, on curved receptors, using three separate angles of view. Sit on your front lawn, parallel to the street, looking straight ahead. You should be able to see the street in your periphery vision (170°). Focus straight ahead and you will see a field of green (unless you live in Arizona) through your normal vision (45°). Concentrate on the details in a blade of grass and you are using only your focused vision (1°). All this without moving your eyes or your head. What we perceive varies from person to person. The camera sees a single flat image through a fixed angle of view. So normal lens perspective will always be a somewhat subjective term. A decent test for normal perspective is to look at a scene with just your eyes, then look at the same scene through the camera’s viewfinder. When you see the same thing both ways you have found your "normal" focal length.
The "normal" lens is different for different film formats. The generally accepted normal lens for 35mm film is 50mm. Mathematically, the equivalent normal lens for most CCD digital cameras should be close to 35mm. When I tested my Nikon D1X and a Fuji S2, I concluded that 60mm provided the closest to normal perspective for me. I then had my mate, Christine, perform the same tests without telling her why. She decided that 35mm was normal. Case closed, normal perspective is subjective.
Some lenses are designated macro and some have a macro switch. Nikon calls their macro lenses micro just to confuse some of us it seems. A macro lens is defined as one that is capable of producing an image on the sensor that is the same size or larger than the actual object being photographed. This is expressed as a reproduction ratio of 1x or 1:1. This life-size "reproduction ratio" should not be confused with lens magnification. Macro lenses come in a variety of focal lengths. A true macro lens is specially designed to allow a shorter than normal minimum focusing distance and projects a very flat image. A close-up attachment will allow closer focusing distances, but at some degradation in image quality. A true micro lens (microphotography) provides greater than life size images (10:1 or more).
There are several other exotic camera lens types. A "fisheye" lens provides a distorted but full 180° view (or more). It gets its name because the extreme curvature makes it look like a fish eye. A "mirror" lens uses a mirror to bounce the light up and down the length of the barrel simulating a longer barrel. This allows construction of a 500mm telephoto lens that is only 150mm long. A fresnel lens will focus a beam of light, typically for a spotlight or light house. Other examples include "tilt/shift" lenses to compensate for perspective distortion. These are also called "PC" lenses for perspective control. A shift lens allows you to change the focal axis while keeping the image sensor plane parallel to the subject. These are used for architecture and flat object photos. Obviously, none of these are simple lenses.
In addition, there are various adapters that may be attached to a lens to change its characteristics. Teleconverters and extension-tubes attach between the lens barrel and the camera body. A teleconverter is an additional lens (or lenses) that extends the base focal length of original lens, making distant objects larger. An extension-tube contains no optics, it merely moves the focal plane, allowing closer focus. They need to be matched to the lens and camera because electrical contact must be propagated. A diopter lens attaches to the front of the lens at the filter ring. Since there are no electronics involved they only need to match the filter ring size. But, they do dictate fixed focusing distances. The name comes from how they are rated.
The basic properties of a simple lens may be applied to an objective lens system as well. They will help us understand the behavior of the lens. But keep in mind the fact that optical design of a complex system is a bit more involved.
Refer to the figure above for a visual illustration of these concepts.
A focal plane is a plane that is parallel to the image plane. There are three focal planes; front, rear, and principal (optical center). They are also called the focal points. The perpendicular axis extending through these focal points is referred to as the focal axis.
The focal length is the distance from the center of the lens to the front or rear focal point along its focal axis. For a simple, symmetric lens these are the same distance. This qualification will become relavent later. The focal length of a lens is determined primarily by the curvature of its surfaces. It is also affected by the index of refraction of the glass and the medium in which the lens resides. The index of refraction is simply the ratio between the speed of light in a vacuum and the speed of light in a given substance. The greater the curvature, the thicker the lens, and the shorter the focal length is.
The image distance describes where an in-focus image of the subject is formed. It can also be described as the point where the rays of light from a distant object converge and are in focus. If the image distance is positive, the image is formed behind the focal plane (typically a convex lens). If it is negative, the image is in front of the focal plane (typically a concave lens). A negative distance image is also referred to as a "virtual image".
An object at infinity is in focus at the focal length. So, the camera and lens are designed such that the principal focal point is one focal length in front of the image sensor when focused at infinity. If the subject of our attention is closer than infinity, (I will call this a nearby object), the focused image is no longer at one focal length. Since this new image distance does not fall on the image sensor, it will be out of focus. Moving the image sensor is not practical and moving the camera or subject is not interesting in this discussion. So, we move the lens, thus moving the relative position of the focal plane(s). This increased distance will put the focused image where the image sensor lies.
The aperture of the lens describes the size of the opening that allows light to pass through. For example, if the focal length were 200mm, a lens opening of 50mm would be F4. A lens opening of 6.25mm would be F32. So, for a given focal length, a larger opening will give you a smaller number. Since the aperture size controls the amount of light that hits the sensor, it directly effects the amount of time (shutter speed) needed for proper exposures. Exposure is discussed extensively in many other photography references. The maximum aperture (smallest number) is important because it directly relates to the maximum amount of light the lens can capture. It will usually also reflect the overall quality of the lens. As the focal length of the lens increases, the diameter of the aperture opening needs to increase to maintain the same F-stop. This is ultimately limited by the diameter of the lens barrel itself. The aperture is frequently positioned as near as mechanically possible to the principal focal plane.
Depth of field (DOF) defines the sharpness of objects that are in front of and behind the main subject. Smaller apertures (larger f-stops) give more DOF while larger apertures give less DOF. But the aperture is not the only variable. In addition the focal length, subject distance, and the circle of confusion all affect DOF. The circle of confusion is a subjective measurement of the smallest detail (single image element) needed so that any blur cannot be detected. Different values are used for different film and digital formats and even for different enlargement objectives. Wide-angle lenses have more DOF than telephoto lenses, other factors remaining constant. But, you have to move back from the subject for the telephoto lens to frame the same image. This almost negates the difference. For example, at F8 a 50mm lens has 4.6 feet DOF with the subject at 10 feet. With a 100mm lens the subject has to be at 18 feet for the same image. At this distance, the 100mm lens yields 4 feet DOF. In summary, DOF can be very critical in extreme close-up photography. Depth of field is discussed much more extensively in many other photography references such as Don Fleming's Depth of Field Articles and my own DOF Demystifying the Confusion so I don't want to spend much time on it here.
The refractive power of a lens is measured in diopters and is equal to the reciprocal of the focal length (1/F) in meters. It is a measurement of the amount that the light bends as it passes through the lens. The shorter the focal length, the more the lens refracts the rays of light. Diopters are used to determine the magnification power of the lens. A one-diopter change increases magnification by 25%.
Lens power is typically indicated by an "X" such as 2X or 4X. Unfortunately there are several different formulas used to convert diopters to power ratings (X). A common measure is "diopters / 4 = power". Another common one is "(diopters / 4) + 1 = power". Using the first formula, a 250mm lens (four diopters) would be 1X and a 25mm lens (forty diopters) would be 10X. Plus, or positive focal powers are called convergent (producing a real image) and minus, or negative powers are called divergent (producing a virtual image). Diopters are commonly used to rate magnifying glasses, microscopes, telescopes, and binoculars. Be aware that some telescope manufacturers define power (X) as the focal length divided by the lens diameter. And some photo lenses define power as the relationship between the focal lengths at the ends of the zoom range. The focal length is the primary measurement used to rate camera lenses.
Because of these different measurement techniques, "X" power is not a consistent way to rate lenses unless you are comparing two models of the same device from the same manufacturer. In addition, the magnification of a lens should not be confused with the reproduction ratio of a projection system. The reproduction ratio is the relationship between the physical size of an image on the film plane and the physical size of the actual object being viewed. It has nothing to do with the size of a print you might make from the photograph. A one to one ratio can be achieved at any focal length with the correct and equal image and object distance. The greater the focal length of the lens, the greater this distance will be.
The Angle of View (AoV), like magnification, is directly related to the focal length. However, to calculate the angle of view you also need to know the size of the image sensor. You can use the horizontal, vertical, or diagonal measurement. When focused at infinity the formula is: AoV = 2 * (arctangent((sensor_size/2) / focal_length)). Thus, using the diagonal measurement, a 50mm lens has an AoV of 46.8° on a 35mm film sensor, but an AoV of 31.7° on a typical CCD sensor. And a 300mm lens has an AoV of 8.2° on a 35mm film sensor, but an AoV of 5.4° on a typical CCD sensor.
When using extreme close-up (macro) focus distances, the magnification (reproduction ratio) needs to be taken into account. This is factored by multiplying the focal length by one plus the reproduction ratio. Since we haven't discussed reproduction ratios yet, I will only state that when focused at infinity it is zero and can be ignored. For macro photography, its affect on the AoV needs to be considered.
The term Field of View is often used interchangeably with angle of view. It shouldn't be. The field of view is a linear measurement that is also dependent on the subject distance. It will also be different when using the horizontal, vertical, or diagonal measurement. The formula is: field_of_view = image_size * ( object_distance / focal_length ) . An example would be a 300mm lens and a subject at 300 feet. The CCD sensor produces a (diagonal) field of view of 28 ft. A 35mm sensor has a field of view of 43 ft with the same lens and subject distance. To achieve a field of view of 28 ft with a subject at 300 ft you need a 450mm lens for the 35mm format. By changing the lens, the image is now larger.
Therefore, the same focal length lens will produce different images depending on the sensor size. This difference between common digital and 35mm film sensor sizes is sometimes referred to as a "cropping factor" and sometimes as the "multiplier effect". It should never be expressed as a "magnification ratio". For example the cropping factor for a Nikon D1X is expressed as 1.5. Thus a 300mm lens on the D1X will frame an image the same as if a 450mm lens was used on a 35mm film camera. It does not mean that the image is magnified the same as a 450mm lens on a 35mm film camera. The angle of view and field of view has changed not the magnification. Similar affects will be observed when using film formats other than 35mm.
Lens specifications usually include the Angle of Coverage. This refers to the circular image of acceptable quality formed behind the lens at infinity focus. It is not dependant on the sensor size.
I must admit that I was easily confused by what should have been simple explanations of lens magnification. The dichotomy was the undeniable fact that a shorter focal length yields higher magnification (power). But a telephoto lens (longer focal length) empirically yields higher magnification. The answer is that the perception of magnification depends on how the lens is used.
With a magnifying glass (loupe), the object is positioned one focal length from the lens and a virtual image is perceived (viewed) from behind, through and in front of the principal focal plane. With a photographic lens, the object is usually many focal lengths from the lens and an inverted real image is projected (approximately) one to two focal lengths behind the lens. Since the photo lens is a projection system, its magnification is dependent on both the focal length and the distance to the projected image.
Magnifying Lens verses Photographic Lens
Therefore, with a magnifying glass a shorter focal length yields more magnification and a smaller field of view. But with a photographic (projection) lens, a shorter focal length yields less magnification with a larger field of view. While the wide-angle lens has a higher power rating, you need to be closer to the subject to achieve the same image size as you would with a telephoto lens. This is called the reproduction ratio. It represents the ratio between the image size on the film plane and the size of the subject.
The simple formula for calculating the reproduction ratio of a camera lens is: R = (I / F) - 1. "F" is the focal length and "I" is the distance from the lens to the image plane. When the focal length and image distance are equal, the lens is focused at infinity and "R" is zero (nil). When the image distance is two times the focal length, "R" is one and the image and object size are equal (1:1). So, as the image distance increases, the reproduction ratio increases. But as the image distance increases, the distance to the in-focus subject decreases. Therefore, we need to explore the lens focusing formulas to complete this analysis.
The basic math behind lens operations is described as the Gaussian simple lens formula:
1 / F = 1 / O + 1 / I
This says that for a given lens focal length (F) there is a direct relationship between the distance to a subject of object (O) and the image (I) that it produces. And, if you know two of these values, you can calculate the third. Of course, all measurements must be in the same system, meters or inches for example. And, for a simple lens all measurements are relative to the optical center (focal plane) of the lens, which is also the physical center of the glass.
Modern camera lenses are actually constructed from multiple pieces of glass (elements). These are usually grouped into sets called element groups. Each element follows the principles of the simple lens formula. Collectively, they follow the principles of the Newtonian thick lens formula.
F1 x F2 = O x I
This measures image and object distance from the front and rear focal points respectively instead of the principal focal plane used in the thin lens formula. For a simple lens, F1 and F2 are the same. So the formula becomes F2 = O x I. For a thin lens, this yields the same answers as the thin lens formula. It does not mean that these formulas can be used interchangeably. We should assume that the front and rear focal lengths and their respective focal points are different. Since these are not published in the lens specifications nor marked on the barrel, we are forced to use the thin lens formulas and use "effective" focal lengths.
There is one more variation of the thin lens formula that might be of interest here.
S = F x ((1 + R)2 / R)
S is the subject distance from the film plane, F is the focal length, and R is the reproduction ratio. This allows focus calculations from the subject distance (near focus limit) and reproduction ratio that is published in many lens user's guides.
More advanced calculations can be made with ray tracing rules and paraxial formulas. Asymmetric lenses utilize front and rear elements of different focal lengths. Formulas to accommodate this will reference the front and exit pupils. There are many more equations, for example the lens maker’s formula. The point of all this is that complex lens assemblies require complex calculations. The objective of this article is to understand the behavior in simple terms, hence we will stick to the simple lens formula.
Enough of this, obviously the lens behavior can be predicted, or at least estimated. The simple lens formula allows us to comprehend the behavior of a simple lens or a complex lens at the same effective focal length. If we know the focal length of the lens and the distance to the image plane we can calculate the subject distance (or conversely). Just be aware that with some lenses the effective focal length can change during focus so your mileage may vary. In addition, most wide-angle and many extreme telephoto lenses have shifted focal planes to conserve precious real estate within the camera or lens barrel. Again, your mileage may vary.
Next I took some crude measurements with my Nikon D1X and my Nikkor Micro 60mm lens. I did not disassemble the lens and the figure is not exactly to scale, so this diagram is not extremely precise, but it does closely approximate the expected measurements. Note that in the following illustration, the principal focal point seems to fall near the exit pupil, not at the center or front of the element array, as I would have expected.
I was unable to perform similar measurements with my Sigma 120-300 zoom lens. The overall length of the lens is approximately 260mm. Add in the 45mm for the camera body and its hard to argue anything but 300mm overall length. The length does not change and the aperture location does not appear to move during zoom or focus. Of course, there are internal element groups that show movement during zoom and focus. I am not going to disassemble the lens just to measure it.
To supplement this analysis, I will take a moment to briefly introduce some of the typical things that can contribute to distortion or degraded quality of the image.
Geometric distortions are manifested by changes in the shape of an image. Three common examples are pincushion, barrel, and keystone. Barrel distortion is unavoidable in super wide-angle (fisheye) lenses. Keystone distortion is usually not strictly a lens defect but caused by not keeping the film plane parallel to the subject. For example, pointing the camera upwards to shoot a tall building.
Spherical aberration is a monochromatic defect that causes the image to appear hazy or blurred and slightly out of focus. This overall haze mimics the similar effects of flare. For lenses made with spherical surfaces, rays which are parallel to the optic axis but at different distances from the optic axis may fail to converge to the same point. This occurs where the outer portions of a lens are optically stronger than the central portion. Spherical aberration can be prevented by using a parabolic rather than a spherical element. These are more complex and expensive to construct. High quality lenses are have at least one of these "aspherical elements". Spherical aberrations can contribute to loss of contrast and vignetting.
Comatic aberration is similar to spherical. It causes rays from an off-axis point of light in the object plane to create a trailing "comet-like" blur directed away from the optic axis. This is most severe when the lens system is out of alignment. A lens with considerable coma may produce a sharp image in the center of the field, but become increasingly blurred toward the edges.
Chromatic aberration occurs because different wavelengths (colors) of light refract at slightly different angles in a given lens. Thus, the red, green, and blue images may not be equally in focus at the same image plane. There are two forms of chromatic aberration, axial (or longitudinal) and lateral (or transverse) aberration. Special achromatic or apochromatic doublet lenses are designed to correct for this. A lens with significant chromatic aberration will show fringes of color at the edges of a subject.
Lens contrast refers to the lens's ability to discriminate tonally between small adjacent areas in the image, lending a sense of texture and surface. Local contrast is the lens's ability to distinguish different tones within a narrow range such as highlight to highlight or shadow to shadow. This is exactly what is "detuned" when you put a "softening" filter on a lens. It should not be confused with the overall contrast (range of lightest to darkest areas) of a scene. Lacking this local contrast, the image will look muddy and lifeless. Flare or loss of luminance can also cause loss of contrast. In general, lenses producing high quality images have both good resolution and high contrast. Other factors being equal, a simpler lens with fewer elements will generally have higher contrast than one with many more elements. This fact is one major reason that prime lenses usually achieve the highest levels of optical quality.
Bokeh is a term used to define the quality of out-of-focus areas in an image. Bokeh is the translation of a Japanese word for blur or fuzzy. The effect depends to a large degree upon the shape of the diaphragm opening and the characteristic circle of confusion of the lens. Bad bokeh may show up as sharp pinpoint round or odd shaped highlights in near or far out of focus areas of the image. Good or bad bokeh is a subjective term since there is no specific scientific measurement. If you see hard-edged, bright, or distracting shapes, you are seeing bad bokeh. If these highlights are soft edged, and non-distracting, you are seeing good bokeh.
Flare is extraneous light falling on the image, scattering and producing a loss of image contrast. It can also produce ghost images and odd light patterns such as hexagonal images of the aperture. Flare can be produced internally within the lens or externally by attachments to the lens. High quality lens coatings are one way manufacturers reduce internal flare significantly. Filters and contaminants on the lens surface can produce flare. Pointing the lens towards a bright light source such as the sun or moon can produce flare. Overexposure can amplify any of these problems. Lens hoods are invaluable at reducing flare from non-image light hitting the front surface of a lens.
Vignette is an artifact that lightens or darkens the edges of an image. Vignette can be caused by using a lens hood that is too long for the focal length of the lens. It can also be caused by using a lens that was designed for a smaller image format than your camera's. Finally, it can be an artifact of a zoom lens with a large zoom range set at its wide angle limit, or an artifact of using the widest aperture possible for a given lens. The reason is that you are pushing the manufacturer's limits for the specific design of the lens. Finally, it can be an artifact of attachments such as teleconverters or extension tubes.
Compound objective lenses are comprised of multiple element groups with different functions such as magnification or focus. Some element groups are used to correct aberrations such as image area curvature and chromatic shift and to improve overall resolution (sharpness). However, more is not always better. Too many element groups can lead to a loss of contrast. These exotic compound lens designs provide manufacturers with the tools to "bend the rules" and provide higher quality, enhanced functions, and lower cost.
Most of these follow variations of the same basic groups. If there is a fixed group it is usually the front element (entrance pupil). It prevents the filter ring from rotating during lens operation. The zoom group (focal length) is generally called the variator. Some zoom lenses have an associated compensator group that helps to maintain focus as the focal length is changed. One or more additional compensator groups provide correction for optical distortion and/or aberrations. The relay group is closest to the body (exit pupil) and forms the final image on the sensor. A retrofocus element is used for super wide-angle and some telephoto lenses to reposition the focal plane of the exit pupil. Without this, the rear element of a wide-angle lenses could interfere with the operation of the camera's viewfinder mirror. For telephoto lenses, it can make the overall lens size shorter than the actual focal length. Internal focus (IF) lenses move the focal plane by moving only one element group, the focus group, instead of moving the entire lens assembly. This reduction in mass and motion reduces the size of the motors needed, improves auto focus speed, and contributes to a smaller or lighter lens assembly. Newer macro lenses may include a Close Range Correction (CRC) or Floating Element (FE) group that adjusts the corrections for aberrations (astigmatism, sharpness) between extreme near and far focus limits. This improves sharpness at close-up distances. The newest group is one used for vibration reduction or image stabilization. This is a movable (rotatable) element that bends the focal axis to counteract motion of the lens barrel.
These compound lenses are further classified as symmetric or asymmetric lenses. A symmetric lens has the same angle of view (focal length) at the entrance and exit pupils. An asymmetric lens has different focal lengths at the entrance and exit pupils. If you observe the aperture from the front and the rear of the lens and it appears to be the same size, the lens is symmetric. It will appear to be different if the lens is asymmetric.
Most camera lenses are compound, complex, and asymmetric to some degree. Therefore, distance information cannot be precisely described by the simple lens formulas alone. The thick lens formula accommodates these complex lenses but the manufacturers rarely publish the detailed information needed to locate the respective focal planes precisely. The overall focal length of the lens system is a function of all the individual elements and the distances between them. This may be used to describe the behavior of the lens with the thin lens formulas.
The final topic here is an introduction to a common measurement of lens quality. Modulation Transfer Function (MTF) measurements assess the contrast between black and white lines of differing thickness or line frequency, and give an objective measurement of a lens’ performance. It is an inseparable measurement of both resolution and contrast. Specialized resolution targets (such as ISO-12233), unique instrumentation, and corresponding software are employed to measure the contrast at several spatial frequencies (line pairs per millimeter). The resulting MTF chart measures contrast and sharpness, it does not measure distortions, flare, color balance, or other metrics.
MTF contrast measures the percentage of the original black and white contrast left after projection. This is typically shown on the vertical axis with distance from the image center (mm) on the horizontal axis. The multiple measurements are then plotted at the different spatial frequencies (lp/mm). 100% MTF is the perfect (unattainable) score. 0% MTF means no detectable contrast difference can be measured. For each frequency there are two measurements, sagital MTF (straight lines) and tangential MTF (concentric circles). Sometimes measurements at different apertures are show on the same chart. Sometimes separate charts are used for different apertures. An example of a 300mm lens at f2.8 and f8 follows:
This is just a snapshot, but all MTF charts will show the same basic trends for any lens. One is that as the spatial frequency (lp/mm) increases, the contrast decreases. The second is that as the aperture changes, the MTF also changes. This is due to a combination of diffraction and optical aberrations. Diffraction is light waves being deflected (fuzziness) as they pass the sharp edges of the aperture. Optical aberrations are a result of larger diameter light beams. Small apertures produce more diffraction but less aberrations. Large apertures produce more aberrations but less diffraction. As a rule of thumb a lens is almost always sharpest at apertures between f8 and f11. Finally, telephoto lenses tend to have flatter MTF curves than wide-angle lenses. That is, wide-angle lenses tend to have less contrast toward the edges. Note that the outer (diagonal) edge of a typical CCD sensor would be at 14mm while 35mm film would be at 21mm. Thus, the CCD sensor is using the "sweeter" area of the lens.
MTF charts can be very useful for evaluating lens quality, especially sharpness. But you must keep in mind that they are not the only measure of quality. And, the MTF charts from one manufacturer may not correlate to similar charts from another manufacturer. When evaluating lens quality you should also consider build quality, focus speed and smoothness, color saturation, bokeh, and features that can be useful for your shooting objectives.
Rags Int., Inc.
204 Trailwood Drive
Euless, TX 76039
December 15, 2003
This page last updated on: Wednesday October 03 2007
You are visitor number 226,551 since 09/01/03