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Stops, Shutter Speed, Aperture, ISO Sensitivity
Posted By: dosdan, 12-18-2010, 12:35 AM

In photography, think of the light as rain (a shower of photons). We are interested in the amount of rain we collect (the exposure). This water volume (exposure) depends on the rate or intensity at which the rain falls (the light level or "scene luminance"), the size of our collection opening (aperture) & the length of time we collect it (the shutter speed). Also, a digital camera can electronically amplify the amount, after collection and conversion to an electronic signal, by increasing the ISO sensitivity (turning up the gain).

For a certain light level, exposure (EV or Exposure Value at ISO100) is composed of the combination of 2 parameters:

f-number:
a relative measure of how big the aperture opening is inside a lens
Shutter Speed: how long the shutter is open

At a set light level, only these two affect the amount of light captured by the camera's sensor. However it is useful to consider ISO sensitivity too since we often operate away from ISO100:

ISO Sensitivity : how much you turn up the gain - like turning up the volume control on an amp: the music gets louder, but so does the noise/hum.
Note: the sensitivity of the sensor is fixed, so it doesn't change as you change the "ISO Sensitivity". It's the gain/amplification of the signal from the sensor that changes.

Manufacturers calibrate the metering in DSLRs to produce a certain rendered image brightness in response to a certain exposure level and a certain amount of signal gain. So, the main role of ISO Sensitivity is to adjust the brightness of the image. Obviously, if the exposure is low, (less photons collected during the exposure period), more gain will be required to render the outputted image with acceptable brightness.

EV is specified at ISO100, whereas the LV (Light Value) incorporates changes in ISO sensitivity. LV at ISO100 has the same value as EV. LV is the average scene luminance (the amount of light reflected off a subject). This is the "brightness" of the scene. Another term for it is Bv (Brightness Value).

It is easiest to think of changes to all 3 Light Value parameters in terms of Photographic Stops. Stops are a power-of-two (doubling/halving) relationship.

Sensitivity
: ISO100 -> ISO200 (+1 stop increase in gain) -> ISO400 (+2 stops from ISO100) -> ISO800 (+3 stops) -> ISO1600 (+4 stops)

Shutter Speed: 1/125s -> 1/250s (-1 stop decrease in shutter duration) -> 1/500s (-2 stops) -> 1/1000s (-3 stops) -> 1/2000s (-4 stops)

F-number to double the area of the aperture, you increase the diameter by root-2 (approx. 1.4).

Consider an increasing root-2 sequence:
1 (root-2^0) -> 1.4 (root-2^1) -> 2 (root-2^2) -> 2.8 (root-2^3) -> 4 (root-2^4)

Each step represents the relative increase in diameter of 1.4 i.e. the doubling of the area of a circle. Now with f-numbers it's the ratio of focal length/entrance pupil diameter, not entrance pupil diameter/FL, so as the f-number increases, the aperture area decreases. For example, 1/2 (one-half) is bigger than 1/4 (one-quarter), just as ƒ/2 (aperture diameter is one-half FL) is a bigger iris area than ƒ/4 (aperture diameter is one-quarter FL).

It is easy to remember the full-stops numbering sequence by remembering just two values: 1 & 1.4. Consider the doubling of each:

1 2 4 8 16 32
1.4 2.8 5.6 11(rounded down) 22

Now combined: 1 1.4 2 2.8 4 5.6 8 11 16 22 32

With this understanding of f-numbers:
Aperture: ƒ/1 -> ƒ/1.4 (-1 stop decrease in aperture area) ->ƒ/2 (-2 stops) -> ƒ/2.8 (-3 stops) -> ƒ/4 (-4 stops)


Here is how varying the exposure parameters affects the output image brightness:

f-number:
Smaller aperture (larger f-number) means less light hitting the sensor, so you either have to increase shutter duration or increase sensitivity (or both) to compensate.
Bigger aperture (smaller f-number) means more light hitting the sensor, so you either have to decrease shutter duration or decrease sensitivity (or both) to compensate.

Shutter Speed:
Faster shutter speed means less light hitting the sensor, so you either have to open up the aperture (smaller f-number) or increase sensitivity (or both) to compensate.
Slower shutter speed means more light hitting the sensor, so you either have to close down the aperture (bigger f-number) or decrease sensitivity (or both) to compensate.

Sensitivity:
Bigger ISO = more gain, so the image brightness increases, as does the noise.
Lower ISO = less gain, so the image brightness decreases, as does the noise.

Now consider the following exposure settings:

1/500s, ƒ/5.6, ISO400.

Assuming the same LV, and keeping ISO constant for the moment, if we increase one parameter by 2 stops, we must decrease the other parameter by 2 stops to maintain the same exposure. The following settings produce the same exposure:

1/125s (+2 stops), ƒ/11 (-2 stops), ISO400
1/500s, ƒ/5.6, ISO400
1/2000s (-2 stops), ƒ/2.8 (+2 stops), ISO400

Now including a change in ISO as well, the following parameters produce the same output image brightness:

1/500s,
ƒ/5.6, ISO400
1/1000s (-1 stop), ƒ/8 (-1 stop), ISO1600 (+2 stops)

I've written an LV calculator so you can use the exposure settings recorded in a image's Exif to roughly determine the light level at a scene. Knowing this will help you to learn which combinations of aperture, shutter speed & sensitivity will work in a particular situation e.g. at the beach or in a circus, so you can plan ahead for the next time.

Excel 2003 LV Calculator

Once you understand stops/LV/EV you can easily determine the amount an exposure changes as you make adjustments. For example, say you want to take a early-morning picture of a water fall or cascade and you want to get a "silky water" effect. This typically requires a shutter speed of 1s or longer. Say your current exposure settings are:

1/8s, ƒ/11, ISO100.

According to the LV calculator, the scene light level that matches these settings is approx. LV 10.

The required change from 1/8s -> 1s for "silky water" = +3 stops because
1/8s -> 1/4s (+1 stop) -> 1/2s (+2 stops) -> 1s (+3 stops)

To get a longer shutter speed there are 4 options:

1. Shoot earlier i.e. pre-dawn, when the LV is lower.

2. Close the aperture further (increase the f-number). A -3 stop reduction in light passing through the aperture is ƒ/11 -> ƒ/16 (-1 stop) -> ƒ/22 (-2 stops) -> ƒ/32 (-3 stops). Now there are two problems here:
a) some lenses don't stop down this far
b) diffraction softening, the reduction in sharpness caused by light passing though a small hole, gradually rises on lenses as the aperture gets smaller and becomes more significant with openings smaller than about f/9.5 on APS-C cameras. By the time we stop down to f/32, we're dealing with a pinhole and diffraction softening is pronounced. On the other hand, with this type of scene, that softening may be acceptable.
3. Decrease the ISO. However many cameras have ISO100 as their lowest ISO so we usually can't go any lower here.

4. Use a Neutral Density Filter on the front of the lens. An ND8 filter = 3 stops light reduction because 2^3 = 8. The exposure setting with the ND8 filter mounted is then:

1/8s,
ƒ/11, ISO100 (LV 10 approx.) - 3 stops (ND8 filter)
= 1s, ƒ/11, ISO100 (LV 7 approx.)


Please note that only the scene luminance, the f-number & the shutter speed determine the actual exposure i.e. the total number of photons falling on the sensor. Increasing ISO sensitivity is different. It does not increase the number of photons hitting the sensor. Instead, it amplifies the voltage after the photons have been converted to electrons by the sensor. Hence, boosting the ISO sensitivity increases the voltage fed into the Analogue-to-Digital Converter (ADC). This boosting also means that any noise that occurs before the ISO sensitivity programmable gain amplifier (PGA) stage, e.g. sensor read noise & photon noise, is also boosted.

Light itself is noisy, as individual photons arrive irregularly. (An irregularity in a supposedly steady signal can be expressed as the presence of a noise component.) At low light levels, photon noise (aka shot noise) is larger compared to the wanted signal, because photon noise rises at the square root of the number of photons captured by the sensor. The reason why a high exposure (more photons captured) is less noisy is that individual photon irregularity tends to be smoothed out as more photons arrive in the collection period.

For example, say only 100 photons (a low exposure level) are captured during the collection period by a sensor's photo-electric element ("sensel"). The square root of that is 10, so the photonic signal-to-noise ratio is 100:10 = 10:1.

Now say 40,000 photons are captured. (A high exposure level - a K-5 sensel can hold a max. of approx. 47,000 electrons.) The photonic SNR in this case is 40,000:200 = 200:1.

Amplifying the sensor output voltage in an attempt to make the digital image look brighter, brings up this photon "shot noise" too. So, in the example above, the low sensel exposure of 100 photons, amplified 400x (+8.6 stops) would still have a photonic SNR of 40,000:4,000 = 10:1.

See the examples of different numbers of photons per sensel here: File:Photon-noise.jpg - Wikipedia, the free encyclopedia

Think about this further. Consider 2 situations:

An average of 32,000 photo-electrons output per sensel, followed by a gain setting of ISO100
An average of 2,000 photon-electrons output per sensel, followed by a gain of ISO1600 (16x relative to ISO100)

Both should result in a similar output brightness level from the ADC. Say the camera has been calibrated so that this is the "Full Scale" (FS) level, i.e. we can't go any higher without clipping the ADC output. As ISO is increased, the number of captured photo-electrons is decreasing (i.e. a lower exposure). Hence the reason why we are increasing the ISO is to increase the brightness of the stored/rendered value in the raw or JPEG image file.

Now compare the shot noise in the two captures:

32000 : root(32000) = 179:1

2000 : root(20000) = 45:1

The reason that the high-ISO (ISO1600) example is noisier than the low-ISO (ISO100) example is not usually because of the use of 16x gain (particularly if the PGA has low noise and minimally degrades the amplified sensor output signal). Rather it is due to the smaller number of photo-electrons capable of being captured before the ADC output clips. As we've seen, a smaller number of photo-electrons means a worse SNR.

This irregularity in the nature of light means that even if a sensor, PGA and ADC all had no other sources of noise, a low exposure will always have more noise, after amplification, than a proper exposure. So the exposure rule is: get the best exposure possible for the required/acceptable depth-of-field & sharpness (the aperture setting) and the required/acceptable level of motion blur (shutter speed), and only increase ISO sensitivity when absolutely necessary.

Finally, the term "exposure". This term is used loosely and incorrectly by many people, probably due to reading books written in the age of film. In the digital age, exposure refers to the amount of photons captured by the sensor, not how brightly the image is rendered after capture. Users who fail to make this distinction consider ISO Sensitivity to be part of the "Exposure Triangle", a term popular in film-era books. But it's not.
The Exposure Triangle is: Scene Luminance; Shutter Speed; f-number.

Dan.

Last edited by dosdan; 03-27-2013 at 03:08 PM.
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11-02-2011, 04:48 AM   #2
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I've added a small section on ISO sensitivity, exposure & photon/shot noise to the end of the article.

Dan

Last edited by dosdan; 11-14-2011 at 05:20 PM.
11-18-2011, 06:36 PM   #3
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Once you understand stops, exposure & LV, you can comprehend the old APEX system (Additive System of Photographic Exposure) from the early 1960s. This was before exposure meters were commonly available. The idea was to estimate the typical scene brightness from a LV chart (see the chart at Tips > Exposure > Light & Exposure Values or Ultimate Exposure Computer), make any adjustment for different film speeds, and you could then set a "LV" dial on the camera which used the right shutter speed and aperture combination for a correct exposure.

This is a stops-based numeric system. The value units are Bv (Brightness Value i.e. scene luminance), Sv (Speed Value i.e. film speed - now, in the DSLR era, better thought of as meaning "Sensitivity Value"), Av (Aperture Value), Tv (Time Value i.e. shutter speed) & Ev (Exposure Value). This is where the terms we use for exposure programs came from, but they are used in a different way nowadays.

These values are defined with the 0 values being:

Sv 0 = ISO3.125
Tv 0 = 1s
Av 0 = ƒ/1
Bv 0 = 1 fL (foot-lamberts, or in metric terms 3.4 candelas/m2). This is at a "K" of 11.4 (explained further down).

Each change in value by 1 value unit is a 1 stop change.

Let's consider an example of f/8, 1/125s, ISO100

ƒ/8 = Av 6 (ƒ/1 -> ƒ/1.4 (1 stop) -> ƒ/2 (2 stops) -> ƒ/2.8 (3 stops) -> ƒ/4 (4 stops) -> ƒ/5.6 (5 stops) -> ƒ/8 (6 stops))
1/125s = Tv 7 (1s -> 1/2s (stop) -> 1/4s (2 stops) -> 1/8s (3 stops) -> 1/15s (4 stops) -> 1/30s (5 stops) -> 1/60s (6 stops) -> 1/125s (7 stops))
ISO100 = Sv 5 (ISO3.125 -> ISO6.25 (1 stop) -> ISO12.5 (2 stops) -> ISO25 (3 stops) -> ISO50 (4 stops) -> ISO 100 (5 stops))

The two APEX equations are:

Bv + Sv = Tv + Av [1]

Ev = Tv + Av [2]

Eqn. 2 reminds us that exposure in the camera is determined by only shutter speed and aperture.

Combining eqns. 1 & 2:

Ev = Bv + Sv [3]

We see that for the same exposure (Ev) settings in the camera, increasing ISO sensitivity (Sv) is used to compensate for decreasing scene luminance/brightness (Bv).

Rearranging eqn. 1 to get Bv by itself:

Bv = Tv + Av - Sv [4]

Substituting our example values:

Bv = Tv 7 + Av 6 - Sv 5 = Bv 8

Bv 8 = 256 foot-lamberts (2^8) or 877 candelas/m2 (metric), at a K of 11.4.

"K" is the reflected-light meter calibration constant. Each manufacturer has some latitude in deciding what K value they'll use in setting their metering level for what they consider a correct exposure. K=11.4 was originally used; nowadays K=12.5 (Canon, Nikon, Sekonic) and 14 (Pentax). Higher K numbers mean that exposure levels are slightly greater today, because the brightness is higher. The increase is 0.13 stops ( K=12.5) and 0.3 stops (K=14). Interestingly, Pentax light metering uses a K which is outside the ISO 2720:1974 standard recommended range for K of 10.6-13.4.

Using a LV calculator (https://www.pentaxforums.com/forums/miscellaneous-articles/88197-excel-2003-l...alculator.html), for ƒ/8, 1/125s, ISO100, we get LV 13. We could have also get this value by using egn. 2 (Ev = Tv 7 + Av 6) since Ev = LV at ISO100.

The difference of 5 value units between Bv 8 & LV 13 is due to Bv coming from a formula which uses a Sv that is referenced to ISO3.125, whereas the formula for LV uses a reference point of ISO100, which is a reference level 5 stops greater.


Dan.

Last edited by dosdan; 05-10-2016 at 04:57 PM.
11-22-2011, 02:39 AM - 1 Like   #4
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An interesting thing about APEX is that it has made a small comeback through being included in the Exif 2.2 specification. So you use an Exif Viewer to see this and easily calculate the LV without needing a LV calculator. I'll use the EXIF View add-on for Firefox in this article ( Exif Viewer - a Mozilla Firefox/Thunderbird Extension). As examples, I'll use the first 4 photos in RonHendriks1966 post:

https://www.pentaxforums.com/forums/pentax-k-5-forum/115277-k-5-sports-photog...ml#post1719538


Here's part of the Exif data from the first photo, shown in list format:

Shot 1:
EXIF Sub IFD

Exposure Time (1 / Shutter Speed) = 1/1000 second ===> 0.001 second
Lens F-Number / F-Stop = 4/1 ===> ƒ/4
Exposure Program = n/a (0)
ISO Speed Ratings = 400
EXIF Version = 0230
Original Date/Time = 2011:11:20 14:38:19
Digitization Date/Time = 2011:11:20 14:38:19
Shutter Speed Value (APEX) = 9965784/1000000
Shutter Speed (Exposure Time) = 1/1000 second
Aperture Value (APEX) = 4/1
Aperture = ƒ/4

First off, don't be misled by ƒ/4 = Av 4 here. That is a coincidence. Av 4 refers to root-2^4 (f/4), while the next two full Av integers refer to root-2^5 (ƒ/5.6 after step rounding due to 1.4 steps) and root-2^6 (ƒ/8). The ISO is in linear form, but the APEX Sv 0 reference is different from ISO100, the LV ISO reference, which we'll be using.

Due to rounding in the standard Tv sequence (e.g. 1/15s -> 1/8s), the actual Tv recorded is a bit messy, but it's easy to see that 9965784/1000000 represents Tv 10.

Using the formula: Ev = Tv + Av

In this image we get:

Ev = Tv 10 + Av 4
= Ev 14

Now this is at ISO100. To get the LV, we need to subtract the stops difference from ISO100 of the actual ISO used. (If ISO100 was used, Ev = LV. If a sensitivity less than ISO100 was used, we need to add the difference e.g. with ISO80 we add 0.3 stops.) The ISO difference here is:

2 stops (ISO100-> ISO200 (1 stop) -> ISO400 (2 stops))

LV = Tv10 + Av 4 - 2 stops
= LV 12

Shot 2:
ISO Speed Ratings = 1000
Shutter Speed Value (APEX) = 9321928/1000000
Shutter Speed (Exposure Time) = 1/640 second
Aperture Value (APEX) = 4970854/1000000
Aperture = ƒ/5.6

The shutter speed shows the choice of 1/3 stop shutter speed increments: Tv 9.3
ƒ/5.6 is Av 5.

The ISO difference from ISO100 is: 3.3 stops (ISO100-> ISO200 (1 stop) -> ISO400 (2 stops) -> ISO800 (3 stops) -> ISO1000 (3.3 stops))

LV = Tv + Av - ISOdiff
= Tv 9.3 + Av 5 - 3.3 stops
= Lv 11

Shot 3:
ISO Speed Ratings = 640
Shutter Speed Value (APEX) = 9643856/1000000
Shutter Speed (Exposure Time) = 1/800 second
Aperture Value (APEX) = 4/1
Aperture = ƒ/4

The ISO difference from ISO100 is: 2.6 stops (ISO100-> ISO200 (1 stop) -> ISO400 (2 stops) -> ISO500 (2.3 stops) -> ISO640 (2.6 stops))

LV = Tv 9.6 + Av 4 - 2.6 stops (approx)
= LV 11

Shot 4:
ISO Speed Ratings = 1250
Shutter Speed Value (APEX) = 9643856/1000000
Shutter Speed (Exposure Time) = 1/800 second
Aperture Value (APEX) = 4/1
Aperture = ƒ/4

The ISO difference from ISO100 is: 3.6 stops (ISO100-> ISO200 (1 stop) -> ISO400 (2 stops) -> ISO800 (3 stops) -> ISO1000 (3.3 stops) ->ISO1250 (3.6 stops))

LV = Tv 9.6 + Av 4 - 3.6 stops
= LV 10

Dan.


Last edited by dosdan; 03-11-2013 at 02:29 PM.
03-09-2014, 06:26 PM   #5
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Here's another go at explaining ISO Sensitivity in DSLRs.

ISO Sensitivity (henceforth referred to here as just "ISO") is the mapping between an exposure level and the recorded brightness level in the digital image file. While ISO changes are implemented by gain changing, ISO itself is about the exposure-to-brightness-level mapping, not the gain per se.

1. First, the exposure is taken. Exposure is the amount of photons/unit area captured by the sensor and converted into an analogue output signal. Exposure is determined solely by Scene Luminance, Shutter Speed, F-stop. It is measured in lux-seconds, lx.s. Both the scene luminance and f-stop affect the "lux" part of "lux-seconds", while the shutter speed obviously affects the "seconds". Lux is a measure of the density rate of photons/s/cm2. which is analogous to the rate the rain of photons is falling on a certain area. Once you multiply this by the exposure period, you get photons/cm2, which is the density of light captured i.e. how much photonic rain was collected in a certain area.

The area of the sensor does not affect the exposure, so, for the same scene luminance, the same f-stop & shutter speed results in the same exposure ,regardless of sensor size. (Technically "t-stop" is the more accurate term to use since a certain amount of light is lost in the transmission through the lens. So a lens set to an f-stop of 2.8 may have an effective t-stop of 3.3.) An FF sensor with these settings and lens will have the same exposure as an APS-C sensor, but due to the 2.3x bigger sensor area of FF, it receives 2.3x more total light for the same exposure, and hence has a potentially 1.2 stops better SNR.

2. Now that the exposure has been captured and converted to an analogue signal, it is amplified to match the ADC input operating window. It is then converted to a Digital Number. The ISO mapping ensures that a certain exposure will result in a certain DN in the digital image file which, when rendered, results a in a certain portrayed relative brightness level. Due to the complexity introduced with matrix exposure metering, where different weightings are given to different light source locations in a scene, there is variation between manufacturers in the exact mapping used. Different cameras have sensor with different quantum efficiencies, metering references & designed-in amounts of clipping headroom, different transmission losses in their Bayer colour filter array filters and different tone response curves. All these affect the ISO mapping used.

Another term for the ISO, particularly in a digital camera, is the Exposure Index. EI reminds us that this value, when applied to the exposure, produces a certain result, i.e. a relative brightness level.

3. In most digital cameras, analogue gain has a secondary role, beside mapping an exposure to a certain brightness level. This is to move the the sensor output level range to a more favourable ADC level range as the exposures decreases. This would not be necessary if the ADC DR performance was better or equal to the sensor DR, i.e. a 14-bit sensor DR into a 14-bit ADC DR since, once the initial matching analogue gain was applied, there would be no need to vary it further with weak exposures – bit-shifting of the ADC output (digital gain) would be all that was needed to increase the rendering brightness as the exposure got weaker.

Unfortunately, a 14-bit ADC usually does not achieve full 14-bit performance, particularly when dealing with the high-speed, low-cost ADCs used in digital cameras. The term ENOB (Effective Number of Bits) is used to express the effective ADC DR. The ENOB can be surprisingly low. For example, Prof. Bob Newman (bobn2), when discussing ADC ENOB performance, claims that:
the 5DIII gives 11 bits maximum though the sensor is giving out 14.5.
(Re: Some corrections/clarification...: Photographic Science and Technology Forum: Digital Photography Review)
Therefore, the more the mismatch between the sensor DR and the ADC ENOB, the more the desirability of adjusting the analogue gain applied in the PGA (Programmable Gain Amplifier) between these 2 stages so as to best suit the smaller optimum ADC input range. Conversely, the more closely the ADC ENOB equals or exceeds the sensor DR, the more closely the imaging system exhibits "ISOless" behaviour.

Dan.

Last edited by dosdan; 12-25-2014 at 07:15 PM.
12-25-2014, 07:15 PM   #6
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If you look at a camera's DxoMark Dynamic Range graph, but in the Screen tab, you will see that this is a proxy indicator of the ENOB performance of the camera's digital imaging system. So for example, the K-5 tops out at 13.6EV. (This is in the Screen tab. In Print tab it's normalised, based on output filesize, to 14.1EV.) So the ENOB performance is close to 13.6 bits for a 14-bit raw file.

Dan.

Last edited by dosdan; 12-25-2014 at 07:39 PM.
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