I have been doing so much research on iso, and for awhile I've been going with the theory that low iso= less noise, so I've been shooting at iso 100 and then adjusting my flashlights and increasing exposure when the photo is coming out too dark. Will i get less noise with a higher iso and a lower exposure time? It's hard for me to tell as I do not shoot cityscapes at night, I create very dark scenes with lit objects. The outside perimeters of my photos are almost always black. Thank you so much. I guess after all the research I still am not sure.
I would say that if your scenes are stationary and you are shooting from a tripod increasing exposure time is the way to go. Also, many recent cameras do a great job at higher ISOs, even upto 1600 (I'm thinking of the D5100 sensors) so you could increase ISO quite a few stops and not be hit. What size do you want to view the photos?
If the scene is static then I tend to favor using lower ISO and longer exposure versus higher ISO and shorter exposure times to do what you describe. By increasing the time of exposure and/or the amount of light you place on the subject, you increase the signal part of the signal to noise ratio (SNR). If the increased exposure time also creates more noise in the shadows, you can always deal with that in post by adjusting the black and/or shadow levels so that anything darker than a threshold you choose will be solid black. When you increase ISO to allow for shorter exposures or less illumination, you are decreasing the amount of signal in the SNR.
Eventually, though, you will reach a point of diminishing returns as very long exposure times (say 15+ seconds or so at room temperature) will raise the temperature of the sensor to the point hot pixels and noise in general will increase. Since these issues are related to sensor temperature, the ambient temperature in the environment you are shooting also plays a part. You can expose longer in a cool environment than in a very hot one before the temperature of the sensor rises to the same level. Allowing time between exposures for the sensor to cool also has an effect.
There is no substitute for some good light.
Noise happens when the electronics in our cameras are stressed, so unless you are pushing your exposure number very high its hard for you to create noise when you keep your ISO numbers low.
So, Will you get less noise with a higher ISO and a lower exposure time?
NO, when 'noise' is in question, you should always spend your ISO last. Our camera sensors are easier stressed when their sensitivity is increased(higher ISO) and the sensor will amplify the effects of noise.
Also, heat has a negative effect on the sensors.. so storing the camera in a cool place or allowing the sensor to cool down after heavy usage before trying to take that tricky shot in question here might help.. even if only by very little.
It depends what you are shooting. For example if you are shooting portraits and the person is still, you should use higher exposure (1/60 is good enough) and lower iso. In my opinion built-in flash makes photos very bright so i'd not reccommend you using flash.
Also, if you are shooting cityscapes with tripod use iso 100 and exposure around 4-5 seconds. higher exposure : light lines from cars. i like that effect on cityscapes also...
In addition to the recommendations of lowering ISO and increasing exposure for tripod cityscapes, landscapes & sky photos, I suggest you use a full-frame camera over a crop sensor camera as, in general, full-frame sensors have larger pixels than cropped sensors*, which in turn gives you less noise.
For example, the Canon 7D (18 MP) has far more noise than the Canon 5DmII (21.1 MP) because the Canon 7D has a smaller sensor and even though it has 3.1 less MP, the sensor is in the 7D is 1.6x smaller than the 5DmII and therefore has smaller pixels.
The formula is conceived by dividing the mega pixels (MP) by the diagonal sensor size (usually in millimetres (mm)). You don't have to do this yourself, there are plenty of websites to help.
It must be noted that sensors by the same company and of the same sensor size (e.g. a Canon full-frame camera vs a Canon full-frame camera) will usually have reduced noise because of an upgraded processor (e.g. Digic 4 versus Digic 5+). For example, the 6D has less noise than the 5DmII not because of the .1µm enlargement in pixel size (which, really, is not enough to make a noticeable difference) but because of the newer Digic 5+ processor is better at reducing noise than the older Digic 4 sensor.
In the same terms, the Canon 7D produces the same noise as the far less expensive Canon T2i due to the fact the processor and the sensor are the exact same (Digic 4 and 1.6x crop sensor).
Rinse and repeat for Nikons.
Pixel pitch for Canons
Personally, I own a 7D and although it has a far superior AF system to the 6D, I do mostly landscape and studio portraits, so I'm looking at buying a full-frame for reduced noise. It doesn't mean the 6D is a better camera, but as reduced noise and larger field-of-view is what I'm looking for, I am considering the move.
Aside: If I had the money, I would buy the 5DmIII over the 6D, to get both an upgrade in both AF and the sensor size compared to the 7D, but I can't afford it.
Pixel pitch for Nikons
Notice how the D800 has such a large MP count, its pixel size is lower than its other full-frame brethren (D700 and D600)? The D800 will thus have more noise in comparison. However, the D800 does have a newer processor, a better AF system, enough pixels that it can be downsampled to reduce the noice and may produce sharper images, so the D700's only feature that may be "better" than the D800 will be its physical larger pixels. Research the cameras for yourself and decide on which features are right for you.
There are plenty of other factors to take into account when buying a camera, but lower pixel size directly corresponds to higher noise.
Best of luck!
* "in general, full-frame sensors have larger pixels than cropped sensors" -- a camera with a higher MP count will reduce the pixel size in relation to the sensor, so I would state this as a "rule of thumb", not absolute fact. Thus, make sure to look up the camera's pixel pitch when in doubt, especially when comparing cameras of the same MP count or sensor size.
** µm = micrometres