I will try to put it simply: TOA radiance is every light which reflects off the planet as seen from space measured in radiance units.

If you look at the planet from space (or if an instrument sensor takes an image) you see what's on the surface, but what you see of the surface it is foggy and bluish. That's because you see (or the sensor registers) mix of light reflected off the surface and off the atmosphere. In fact in the blue region of visible light, greater part of the light comes from atmosphere than from the surface.

Atmospheric correction is then a method how to try to remove influence of just that portion of light reflected off atmosphere on the image and preserve the part reflected off the surface below (simplified to get the idea, because atmosphere does more than just reflecting part of the incoming light).

This way you get BOA (bottom of atmosphere) or surface radiance. The same applies to TOA and BOA/surface reflectance.

http://webcache.googleusercontent.com/search?q=cache:zpofUnjqb_YJ:www.mdpi.com/2072-4292/7/6/8019/pdf+&cd=2&hl=en&ct=clnk&gl=sa

http://semiautomaticclassificationmanual.readthedocs.io/en/latest/Landsat_conversion.html

http://www.harrisgeospatial.com/Home/NewsUpdates/TabId/170/ArtMID/735/ArticleID/13592/Digital-Number-Radiance-and-Reflectance.aspx

http://www.rsgis.ait.ac.th/~honda/textbooks/advrs/DN2Reflectance_2p.pdf

Thank you

TOA is the reflectance that has not been corrected atmospherically. 

Reflectance is dimensionless because radiance is divided by irradiance so the units cancel. However (and this confuses many people) reflectance is not constrained to fall between 0-1; sometimes it is stored in integer format (e.g. 12-bit or 16- bit) because floating point format (0-1) takes up too much disk space. 

If you have pixel values of 1000 then the data can certainly be in top-of-atmosphere or surface reflectance. However, you need to look at the metadata and/or read the data description to be certain what level of processing the data had. Do not look at the data and try to make guesses about the processing - the level of processing is explained in the data documentation.

If you are using Landsat climate data record (CDR) data then it is mostly in surface reflectance but it needs to be slightly rescaled as well as have a sun angle correction applied. If the data was distributed as TOA reflectance then the radiance at the Landsat sensor was divided by the exo-atmospheric irradiance and this is better than nothing but there will be band-specific biases (according to Rayleigh scattering). 

What downloaded from USGS has DN values, that does not lie within 0 - 1, unless you downloaded their SR products. It can be seen directly from the file names or from the metadata or dataset you have selected before downloading.

Otherwise, you have to convert DN into TOP using any RS based software automatically and manually. I tried that in ENVI using Radiometric Calibration, it work fine. You just need:

Thats all. For theory consider the following research paper (link to pdf added).

While surface reflectance (SR), is opposite to Top of Atmosphere reflectance (TOA). As SR is the measure of reflectance on the surface of the ground as compare to reflectance measurement at the sensor in case of TOA for general understanding. Consider the following link (surface reflectance by Pancroma.com).  

https://www.google.com.pk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=0ahUKEwiri4_m-t7RAhUCmBoKHVM_BzMQFggZMAA&url=http%3A%2F%2Fwww.pancroma.com%2Fdownloads%2FApproximating%2520Landsat%2520Surface%2520Reflectance.pdf&usg=AFQjCNHUj1oiVfWZqTVAVygYKgpda9ayBQ&sig2=cwGbl22NdYn-h8J9zQ7vuA

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20090027884.pdf

Article Summary of current radiometric calibration coefficients for ...

For ENVI:

http://www.harrisgeospatial.com/Home/NewsUpdates/TabId/170/ArtMID/735/ArticleID/13592/Digital-Number-Radiance-and-Reflectance.aspx

This is best link to understand the theory. Hope it helps. 

Thank you very much

Sorry, but I still don't get the definition of TOA radiance. Any help?

I will try to put it simply: TOA radiance is every light which reflects off the planet as seen from space measured in radiance units.

If you look at the planet from space (or if an instrument sensor takes an image) you see what's on the surface, but what you see of the surface it is foggy and bluish. That's because you see (or the sensor registers) mix of light reflected off the surface and off the atmosphere. In fact in the blue region of visible light, greater part of the light comes from atmosphere than from the surface.

Atmospheric correction is then a method how to try to remove influence of just that portion of light reflected off atmosphere on the image and preserve the part reflected off the surface below (simplified to get the idea, because atmosphere does more than just reflecting part of the incoming light).

This way you get BOA (bottom of atmosphere) or surface radiance. The same applies to TOA and BOA/surface reflectance.

Our paper, "A survival guide to Landsat preprocessing" may be useful for people seeking further clarification on these questions:

Article A survival guide to Landsat preprocessing

Dear I hope this will help you to understand the different

Top of the Atmosphere (TOA)

Digital Number (DN)

Digital Number (DN) is the generic term used for pixel values. These values correlate with the energy that is observed and measured at the sensor. Although the DNs are related to the surface reflectance values, they are not the same. Depending on the purpose of the study, comparing DNs acquired by a satellite, without correcting for atmospheric effects, can lead to problems - even if the Landsat DNs have been calibrated and processed.

Radiance, Reflectance, and Top of Atmosphere (TOA)

Radiance is directly measured by remote sensing instruments. Radiance includes the radiation reflected from the surface, in addition to the radiation that bounces in from neighboring pixels, and the radiation reflected from clouds. Radiance is dependent on not only the illumination (both its intensity and direction), but the orientation and position of the target also. In other words, the path of light through the atmosphere can change as the light travels down to the earth through the atmosphere, suffering wavelength-dependent scattering. The light then diffusively reflects off of the Earth's surface (Figure 1), travelling back up through the Earth's atmosphere, enduring further scattering effects as it does so. Some of these factors can be corrected by using Top of Atmosphere (TOA) reflectance values, instead of DNs.

My regards

Interesting

Thanks sir so much Tomáš Brunclík !

Now I quite understand the definition of TOA,

Besides, please explain the BOA to us.

Thanks

Can Trong Nguyen, BOA (Bottom of atmosphere) radiance should equal to radiance measured in-situ, as you would normally do with a radiometer, standing on the surface and measuring the light reflected off the surface. In case of in-situ reflectance, the measuring instrument measures reflected light off the surface and incoming light from sun and the sky on the site and computes reflectance. BOA spectral radiance or reflectance should depend just on the material and conditions (such as moisture content) of the reflecting surface and is not influenced by atmospheric conditions.

In satellite images, atmospheric correction should remove atmospheric effects on the pixel values and often also some other effects. The result is called Level-2 satellite image or BOA image. It is however good to keep in mind, that it has pixel values with just estimation of BOA radiance or reflectance as it would be measured in-situ with spectroradiometer and the values may still be affected by residual uncorrected atmospheric effects or, on the contrary, by "overcorrection" as well as by adjacency effects, directional effects, possibly by some deficiencies of the satellite sensor etc. In other words, radiometric precision of satellite image would never reach the level of precision available when measuring in situ and varies with methods of atmospheric correction and quality of input data used in the process.

Hello, i hope you have came across with the definition of this concepts, but in case that someone did not:

The difference is that TOA radiance has included radiation reflected in the atmosphere (to the sensor) before going trough it and radiation reflected by the target that interacts with the atmosphere on it's way out to the sensor. The radiation that reflects in the atmosphere before going through it is taken as constant for the different bands. The interactions of the radiation reflected from the target with the atmosphere are descripted by the different types of scattering and this effects are what you assess when you perform atmospheric correction; so, surface radiance is TOA radiance with an atmospheric correction.

The units are W/m2.sr (watts divided by square meters multiplied by steradian) in the especific band that you are dealing with. The stereoradian has to do with the instantaneous field of view of the sensor. The units correspond to energy flux by surface unit and by solid angle unit.

The ranges are the same, but when you perform the atmospheric corrections values tend to change on the visible range, especially near blue because of rayleigh scattering and on the infrarred range, e.g. after DOS substraction. Values are around 1000.

The values of reflectance must be divided to get values between 0 and 1. Normally you have to divide by 10000 and this is because of the size of the file when you include decimal positions (multiplying by 10000 eliminates decimal points and it is easy for the data user to divide by 10000 later, causes no information loss).

I hope this might be useful to someone,

Regards

I'm sorry i have to correct something i said. Values of radiance are not around 1000, they are around 10.

thank you Matias for that information

but is there a reference for dividing the reflectance values by 10000? I need it please

Hello Doaa, i can assure you that reflectance values have sense when you use this factor (they range from 0 to 1, or from 0 to 100 if they are expressed in percentage) but i can not give you a reference, you may have to look in the product guide of the data you are using

Usually reflectance raster or grided data are multiplied by a factor so that the distributed values are integer numbers which do no lose the relevant decimals in the original values. Check your reflectance data source product description for these factors.