One characteristic that we can use to describe a sensor that's used for remote sensing is the radiometric resolution. Radiometric resolution refers to the range of numbers that a sensor uses to record reflected light, sometimes that's referred to as the quantisation level. So, a larger range means that you potentially are able to record more data that can be turned into better information. Essentially, just think of it like this for now, is that imagine if you have a range of values from 1-10. So, one is no light being reflected, 10 is the most being light reflected. So, you've divided up the amount of light that you're recording into 10 possible categories or numbers. That doesn't give you a huge amount of range of difference between those, between, say five, or six, or whatever; but if you had a range from 1-100, then you have a finer scale, you have more possible numbers that can be used to describe the light being reflected from something. What if you had it from 1-1,000? That would be a higher radiometric resolution. That would be a higher quantisation level. So, essentially, what's happening here, just remember, is that you have light reflecting off of an object, the sensor is recording that and it's turning it into a number. So, whenever we say a number, the whole point is what's the range of numbers that are possible for that? Is it a small range of numbers? Is it a large range of numbers? That has to do with the radiometric resolution. The way the radiometric resolution is often described is in terms of the number of bits that are stored, and so I think in order for this to make a little more sense to you I'm going to do a little review. I know this is going to seem really basic for some of you on exponents, and then how we count with 10s, and then we're going to help to see how we count with twos; and just kind of a review and make sure everyone's clear about how bits are created, how they're used to count, and how that relates to imagery and how that ultimately relates to how much information we're able to extract from an image. So, if we have a number to the exponent zero. So, x to the 0. Anything that's a number to the 0 will equal 1. So, 2 to the 0 equals 1, 3 to the 0 equals 1, anything to the 0 equals 1. Any number to the exponent of 1 is equal to that number. So, 2 to the power of 1 is 2, 3 to the power of 1 is 3. So, then, we go into things like x squared. So, x to the power of 2, that's x times itself. So, x times x is the same as saying x squared. So, 2 to the power of 2 is the same as saying 2 times 2 equals 4. So, x to the power 3 is the same as saying x times x times x. So, 2 to the power of 3 would be 2 times 2 times 2, which is eight. So, this brings us to how we normally count numbers, which is using a base ten system or a decimal counting system, and that just means that we're counting by tens. So, if we have the number five, that's in our ones column. So, if you think back to, I don't know, probably elementary school and you have the ones column, the tens column, the hundreds column, the thousands column, that's what we're talking about here. So, we have a number in the ones column. In this case, it's a 5. So, how do we actually describe that in terms of what I was just saying about exponents? So, that would be the same as saying 5 times 10 to the power of 0. So, that equals 5. So, remember, 10 to the power of 0. So, 5 times 10 to the power 0 is the same as saying five. In the next column, the tens column, if we have a two, that's the same as saying 2 times 10 to the power of 1 equals 20. So, if we add those two together, we have 20 plus 5 equals 25. If we go to the hundreds column and we have a one there, that's 1 times 10 to the power of 2, and so that's 100. So, now we have 100 plus 20 plus 5 is 125. So, with these three categories of numbers, the 100s, the tens and the ones because we can have a value from 0-9 in each of them, that's ten possible values, that together we have 10 times 10 times 10 which is 1,000 possible values, which is 0-999. So, the pattern I want you to see here is that we have a 10 to the 0 there, 10 to the 1 there and 10 to the 2 there. If we add the next one over, that would be 10 to the 3. If we had another one over here, that would be 10 to the 4. So, that's the basis for our counting with our base ten system. Now, let us look at the way computers like to count, which is a little bit different, and this may be a big flash back for anyone who's older and remembers these. They're actually a little bit before my time, but I do remember seeing them around. These are punch cards,and this is a way that computers, long time ago, stored data, was based on whether there was a whole punch to the particular location in the card. So, basically, something was either punched or not punched, and that was the way that they were able to record data with this card that was organized in a certain way. So, we can think of that as the twos possible states are punched or not punched. You can also think of that as whether something is on or off, or whether it's a one or a zero. So, I'm sure this is probably relatively familiar to you in terms of how computers like to think or work, is that they're either a one or a zero. So, these are referred to as binary digits. So, binary just means two or there's two possibilities. So, in this case, there's only two ways to describe this. It's either as a one or a zero, on or off. So, a binary digit. Which by the way, I don't know if you know this, but the short form for binary digit is bit, and so that's where the term bit comes from is binary digits. So, a bit is a bit of stored data, pardon there, that's either in a state of one or zero, on or off. One thing that's, I don't know if you know this, whenever I tell students this is, there is always a few people that are blown away, is that if you see something like this on a computer or somewhere else, that symbol, what that is is that's a zero and a one. So, that's the one and the zero there. That's what that power symbol actually means, is that there's really only two states, either the power is on and it's a one, or the power is off and it's a zero. So, one or zero, on or off, binary digit, bit. So, if computers like to work with this very simple fundamental system of ones and zeros, ons and offs, then we can think of that in terms of well, how would a counter then count up numbers? It's not going to count by tens, it's going to count by twos. The twos being zero, one, the two possible states. So, here we have a light switch, and so it can either be off as a zero or it can be on as a one. So, there's two possible values, zero or one. Now, imagine I just changed that from a light switch to a number. So, I say this is a zero when it's a one. So, this is going to be my ones column for the way that we're going to count here in our binary system. So, if we wanted to describe that according to exponents, this would be the same as saying 1 times 2 to the power of 0. That would be equal to one. So zero times two to the zero equals zero, one times two to the zero equals one. So if we only counted with this one column, there's only two possible values that we can have, either a zero or a one. So, why am I telling you all this? If we look at an image, the way that the image can be described or the sensor could be described, they created this image is based on the radiometric resolution. What's the range of possible values that were used to collect data based on how much light is being reflected? If we only had a one bit image, that's how this would be described, then there are only two possible values for the cells, that are either zeros or ones. So we have a very limited amount of data here to work with and that means it's hard for us to interpret this and turn that into information. All we can really say is that while there's areas that are dark and there's areas that are light. That's it. So obviously, this is kind of an extreme example but I want to start with this so you kind of see the advantages as we go to higher bit images that have a higher radiometric resolution. So what if we add a second column to this, so now we can count using two possible numbers. So in this column we have a one. This is our ones' column. So we have one times two to the zero. That gives us a one, and in this column we have a one. Now, this is where things can get a little bit confusing if you're not familiar with this. This is not the tens column. That's not the number 11, okay? That's the twos column because remember we're counting based on a binary system of ones and zeros. So that would be the same as saying one times two to the power of one, which would be the value, two. So if we added those together, two plus one would equal three. So we can have two zeros, we can have a zero and a one,a one and a zero, a one and one, and so we now have, if we have two columns here are based on accounting system, that's based on two's, where we have four possible values, okay? So we have- remember a bit is either a one or a zero, so now we have two bets because we have two combinations of ones and zeros. So this is now a two bit number. So now if we go back to the same image but now we have a two bit version of that, we have a higher radiometric resolution. We now have values between zero and three's, so that's four possible values. Now we're getting a little bit more information here. We're able to see that we have areas that are bright, we have areas that are dark like here, and then we have areas that are in-between. There's actually four possible values but there's only three that are kind of obvious to us here. So that gives us more data, more information to work with because we've increased the radiometric resolution. So let's go back and increase it again. If we have four bits, so we have four possible numbers that are either zero or one. So now let's say we have a one. That's a ones column, one times two to the zero. Here we have a zero in a two's column, that's zero times two to the one, that's a zero. Now we have a one here. So that's our fours column. So that's one times two to the two, that's four. Then we have our eights column, that's one times two to the three and that's eight. So the key here, the reason I'm showing this partially, is to recognize that there's a similar pattern to what we had with counting by tens. If you look at the exponents, we have a zero, a one, a two and a three, but instead of counting by ten here, we're counting by two. So it's two to the zero, two to the one, two to the two. That's the basis for this counting system,okay? So when we see something like this, one one zero one, remember, this is not thousands hundreds thousands or tens and ones. This is eights fours twos and ones. So if we added this together, eight plus four plus one equals 13. So now, we have two times two times two times two is 16 possible values and I've actually listed all of them here so these are all the possible combinations of zero and one that can be used to describe 16 different values from zero to 15. So now if we go to our same image again, but now this is a 4-bit radiometric resolution and I'm hoping that you're seeing what's happening here is we now have even more data, even more information that can be extracted from there. So now we're not only seeing light and dark or light, dark and medium, we're seeing upgradation of values from zero to 15. So now we're able to pick up more nuanced things so we're getting different types of values in here, along this river, here, this is the downtown Toronto area here and so we're able to actually start picking out roads and parks and water. So again the idea being higher radiometric resolution because we have more bits to work with, means that we're more likely to be able to extract more information from that image. Last example, if we go to eight bits here, so we have ones, twos, fours, eights, 16's, 32's 64's and 128's. So it's exactly the same pattern here. I've just continued it on. So we have two to the zero, one, two, three and so on and so in this particular example here, if we added this up this gives us a value of 215. So this is eight bits together. So remember, each bit is just a one or zero. We can have one bit, two bit, four bit and so on, and so here we have eight possible combinations. So this would be considered an eight bit number. So here we have two times two times two times two. This here is like two to the eighth. So we have 256 possible values which are from zero to 255. By the way, this is a very common counting scheme that's been used over a long period of time. A lot of older imagery especially you'll find has an eight-bit radiometric resolution, so a lot of the data that I've worked with for many years is from zero to 255. So that's a common way to to see that. By the way, when computer scientists we're developing this, they decided that 8-bits was a useful number of bits to be able to use to characterize or to code alpha-numeric characters like numbers and letters and so I don't know- I think this was meant to be kind of a tongue-in-cheek joke, but they decided that they would call eight bits, a byte. So bits and bytes, and so you may have heard that expression before two other term, is that if you have a number that's based on a bits, that's also referred to as a byte. So here we have our eight bit image. So this is the actual real radiometric resolution of this image which was from Landsat seven because it's an 8-bit sensor and so we have values from zero to 255 and obviously now, we're able to pick out even more detail. We have more numbers to work with, with a higher range of possible values and we can extract even more information from this. So just to summarize these, you get the idea, so I've shown you a one bit, two bit, four bit and eight bit version of the same image. Remember, the whole point of remote sensing is you're trying to extract information based on light that's reflected, but in order to do that, you have to be able to have a range of values to work with in order to maximize what you might be able to extract. This is a quote from the NASA website before Landsat eight was launched. I included it here because I think it's a nice way of illustrating the importance of radiometric resolution. So what they say here is one improvement will be greater sensitivity. This is for Landsat eight which at the time was before it was launched was referred to as the Landsat Data Continuity Mission. So they say when approval will be greater sensitivity. Landsat seven measures the amount of reflected light on a scale of zero to 255, 8 bits. Well LDCM will measure light on a scale of zero to 4,095, 12 bits. This improvement will enable researchers to better characterize land cover and land use on a global scale. So Landsat seven was eight bits, Landsat eight is 12 bits and so you can see that there's a much larger range of possible values, which just makes it much better and more likely that they we'll be able to extract better information from Landsat eight images than we were able to do with Landsat seven.
