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Opening Aperture: f22

Opening Aperture: f45

In the previous article diffraction theory for circular targets, it was established that a separation between the centers of the Airy disks of:

d = 1.22 fλ

guaranteed, according to the Rayleigh criterion, two points of light very close to be resolved as different points in the image and do not constitute a single oval of light, something that obviously hurts their sharpness.

It is time to understand what are the practical implications of this statement.

If we take an APS-C sensor typical 23.6 mm. wide by 15.8 mm. high that contains within it a pattern of 3872 x 2952 fotocaptores of light, is quite simple to calculate what the estimated separation between the captors.

horizontal separation = 23.6 / 3872 = 0.0061 mm.

vertical separation = 15.8 / 2952 = 0.0054 mm.

As these results are merely estimates, we can say that the separation is about 0.006 mm.

If the incident light is predominantly bluish tint, which is most common in outdoor photography, its wavelength is about 0.0004 mm.

With these data we are able to estimate the number f that guarantee the Rayleigh criterion. If we use a value of f11, then:

d = 1.22 x 11 x 0.0004 = 0.0054 mm.

Therefore, with this value for the number f, the distance between the centers of the Airy disk is less than fotocaptores existing between two points ahead and the image is properly solved.

In the heading of the article are two pictures taken at exactly the same conditions using a tripod, remote shutter release and the Tamron 90 mm macro lens. f2.8.

The only difference is that in the first of them has used an f value of 22 and the second a 45. It is clear that, despite being a value significantly steeper than the threshold corresponding to f11, the former is not observable a noticeable loss of sharpness, while the second does. The f values \u200b\u200bfor these numbers are:

d22 = 1.22 x 22 x 0.0004 = 0.011

, D45 = 1.22 x 45 x 0.0004 = 0.022

In the first case the distance is about twice that which exists between two consecutive fotocaptores. The second is four times larger.

Just keep in mind that the above calculations are merely estimates and their only intention is to give a qualitative approach to the problem, without trying to be absolutely accurate.

Finally, it should be noted that the title of the article is related to the fact that these so closed diaphragms are only used in practice photomacrographs.

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photomacrographs Diffraction and Diffraction in photography tripods

When light shines on the corners of an object or through an opening in it, is diffracted, which means that it shows an interference pattern consisting of alternating light areas and shade. In the event that the opening is approximately circular, so as forming the diaphragm, these zones are concentric rings. Yes a size very very small. In our everyday experience diffraction is the cause of that area intemedia in brightness between the parties strongly illuminated by the sun and the darker areas, which sometimes occurs in the corners of buildings.

The figure accompanying this article, we assess the situation in which the infinite light from passing through the lens exposed through an aperture of diameter D. Under these conditions, the camera sensor must be located at a distance F, corresponding to the lens focal length, if we get a sharp image. When light passes
creates inteferencia pattern above, which is a first illuminated circle (called Airy disc) and a series of concentric rings alternating dark and bright concentric rings. The brightness of these rings fell sharply as we go away from the center. Is what the wave shown in the diagram. The theory of Fraunhofer diffraction (Optica. Hecht-Zajac, American Educational Fund, pp.372-375) states that, for circular cracks, the angle θ formed by the lens optical axis and the starting position of the first ring Dark is calculated using the formula: λ

Θ = 1.22 ---

D

where λ is the wavelength of incident light .
If we have two very close light rays, the diffraction patterns will overlap. If they are really close, the two respective Airy Physicians will overlap and two points of light will be indistinguishable in the sensor. Form a continuous oval. The Rayleigh criterion states that for both points of light can be distinguished, the centers of the respective Airy discs should be separate at least by the radius of any of them. (We must remember, as shown in the figure, even within the Airy ring, the luminosity drops sharply as we move away from downtown).
Therefore, the separation d - as also seen in the figure - is expressed by the following formula (Bearing in mind that for very small angles senθ is approximately equal to θ) d = F



Substituting θ in above formula, we find that:

λ F d = 1.22

D ---

But it appears that the ratio F / f D is the number for that opening.
From which we have the exprexión:

d = 1.22 λ f

which allows us to calculate the distance between the centers of the Airy disk, for two rays of light coming so they can be resolved as two distinct and not be mistaken as a single point of light.
In the next article we will the practical consequences of this formula.

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We ask two questions:
a) Is it important to have an exact placement, either horizontally or vertically, when we take our pictures?
b) If yes, how?
On the first point I will pursue a strategy similar to that followed in mathematical proofs by contradiction. In them. is part of one or more hypotheses, following the relevant arguments and arrive at a contradiction, we will have shown the invalidity of the premises.
What happens if an adequate level of camera?. In fact, in most cases nothing. But there are certain special cases in which the placement is critical. In my personal experience, two situations like this are what I set out below.
One is the making of subjects that occupy much of the frame using a wide angle, usually a building. In this case, if the flatness is not perfect, when we performed the alignment by the editor and activate the subsequent crop, there is a risk that the composition is seriously committed to "cut" any subject area.
The other, perhaps more importantly, is the production of panoramas. Here, if the grading is not adequate, we run two risks. The first is that it is necessary to marry the different takes by hand, since the software may encounter difficulties when trying to do it automatically. Certainly is a cumbersome task. Furthermore, in the final cut we can, as in the previous case, losing the intended composition.
surely more experienced photographers might propose other circumstances in which an appropriate placement is appropriate. Get
leveling is perfect, as is obvious, if we use the camera impossible show of hands, but it is possible using a tripod.
In a previous article on tripods at the end the following sliding Comment:
" One last item I want to say is the presence of a level to achieve perfect flatness. I know that many photographers consider it an important element, but I personally I have not ever found any use ."
This comment reflected the difficulty in obtaining suitable placement if the level was on the tripod. In fact, the only way to achieve this is to stretch or shrink the legs in a trial and error.
time ago, due to the emergence of some slack in the kneecap that initially bought, I bought a new one that incorporates two levels. And the situation varies significantly. Indeed
leveling de un plano se consigue utilizando únicamente dos de los tres grados de libertad que proporciona la rótula. El grado de libertad proporcionado por el giro en un plano horizontal al suelo (o vertical, depende de la posición que adopte la cámara) presupone la horizontalidad ( o verticalidad) de ese plano. Por tanto son los otros dos grados de libertad los que garantizan esta situación. Si disponemos de niveles para ambos, podremos asegurar la adecuada nivelación de nuestras fotografías.

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Equalization in Depth of Field and Focus Distance

Para conocer cómo varía la Profundidad de Campo en función de la Distancia de Enfoque, deberemos basarnos en un par de cosas que ya conocemos, a saber:
a) El tamaño del círculo de confusión depends exclusively on the size of the sensor.
(See the article on the Circle of Confusion).
b) The thin lens equation can be expressed as q = pf / ((p - f).
where:
p is the distance from the objective focal plane.
f is the lens focal length.
q is the distance the image plane, corresponding to the focal plane, the target.
(See article on thin lenses.)
From the knowledge of these facts and taking the example of a normal lens 35 mm for the APS-C, we obtain the value of q for three different focal planes, one located at 100m (100000 mm), one located 10 m (10000 mm) and a third at 1 m (1000 mm) .
q1 = (100000. 35) / (100000 - 35) = 35.01
q2 = (10000. 35) / (10000 - 35) = 35.12
q3 = (1000. 35) / (1000-1935) = 36.27
" do these results mean? Well
focus levels between 100 m and 10 m are their images in a range of
35.12 - 35.01 = 0.11 mm.
and focus levels between 10 m and 1 m are their images in a range of
36.27 - 35.12 = 1.15 mm.
This means that the density of levels is much higher in the first interval in the second. Since, a constant aperture, double inverted cone to a point defined image plane for the circle of confusion is the same, within double inverted cone that are located many more flat image in the first case than in the second and, therefore, the depth of field is greater.
Therefore, we can establish the following rule:
a) If the focus distance increases, the depth of field.
b) If the distance decreases Focus decreasing the depth of field.
This is why the very small depth of field found in the field of photography.