Daido Moriyama

" Cities are enormous bodies of people's desires, and as I search for my own desires within them, I slice into time, seeing the moment. That's the kind of camera work that I do."

-- Daido Moriyama

Baby in a crate

The curious one

When all the brain-washed look to one direction, the curious one looks the other way.

Struggling to survive

Vega Omer's famous black and white photo, "Struggling to survive". Very powerful message.

Understanding aperture: The 3 types, when to use them, and why

Aperture can feel like a tricky beast at first. But once you have a sense of what it is — the idea of depth of field — it’s time to look at how to put these tools to use for your own vision with photography.
Even though f-stops number from f/1.4 to upwards of f/22, aperture can be divided into three major sections, each with its own distinct use. Which section and corresponding f-stop you choose becomes up to you, and your vision.

Storytelling

What it is: Storytelling aperture is considered to be f/13 and up, as high as f/22, or f/29 on some lenses. If you can recall, the higher the f-stop, the smaller the aperture, and the greater depth of field. This means the image should have front-to-back sharpness.
Uses: This is often used in landscape photography, where you want the foreground just as much in focus as the background. If you’re telling a story, then you need a foreground object, a middle ground, and a background, all of which “lead” your viewer through the image. This could be a dirt road (foreground) leading up to a barn (middle) with puffy white clouds behind (background). It could be a jagged rock (foreground) in a calm, clear lake (middle) backing into the Grand Tetons (background).
Alternative uses: Higher f-stops are often used at night because the tiny pin-hole aperture makes any point of light (i.e., a streetlamp) turn into a starburst. To compensate though, the shutter speed needs to be long and therefore a tripod is necessary.
Do not use for: Faces. Higher f-stops are simply not flattering on the human face.
Drawbacks: When everything is in focus, you need to make sure your viewer knows exactly what your subject is. If it’s not going to be the object most in focus, then you have to use leading lines, composition, and/or light to reveal the subject of the image.
Remember: The higher the f-stop, the less the light. Therefore you need to lower your shutter speed (or use Av and the camera will do it for you), which could mean that you need a tripod if it goes under 1/50. Alternatively, you can boost your ISO, but this adds noise to the image.
Best lens: A wide angle lens (roughly 10mm-20mm) will allow you to fit the whole story into the scene.

The sweet spot

What it is: The range is roughly f/7.1 – f/11. It is said, and overall believed to be true, that f/9 or f/11 are the “sweet spots” on any given lens. That means they have optimum sharpness, contrast, colour, and least amount of lens distortion or aberration.
Uses: These stops are great for street photography and shooting on the move. Overall they are sharp, usually give nice contrast, and generally maximize the optics of the lens in use. They can be put to use for landscapes, street scenes, scenes with people in them, or any other situation in which your “subject” might change quickly (say from a purple door, to a man pushing a cart, with little time to change settings).
Alternative uses: Sunrises and sunsets, where you want overall sharpness and contrast. Also, night scenes where you’re not looking for starbursts but want good sharpness.
Don’t use for: Faces. Even f/7.1 still isn’t the most flattering for portraits.
Remember: Both “storytelling” and “sweet spot” apertures will be hard to work with inside, under shade, or any time the light starts to drop. Same as with “storytelling,” it is up to you to make sure the viewer knows what the subject of the image is, using techniques other than isolation.
Best lens: If you are aiming for street photography, a semi-zoom is the best bet (e.g., 24mm-70mm or 18mm-200mm) to allow you to pull out and back in, as your subjects change. However, in terms of shooting at f/9 or f/11, it’s the sweet spot on nearly any lens.

Isolation

What it is: Apertures under f/5.6, all the way down to f/1.2. The lower the f-stop, the more wide open the aperture, the more shallow the depth of field.
Uses: The main use of a wide aperture is to isolate a subject. When you focus in on your subject — say, a person’s face — the background will blur. This blur can range from slightly out of focus (e.g., f/4) to completely unrecognizable (e.g., f/1.4). When the subject is isolated, it’s very clear to the viewer what the subject of the photo is, which can make for very strong images. It is flattering on faces because of the softer focus, but be sure to focus on the eyes!
Other uses: Lenses that are 2.8 and under are called “fast” lenses. This is because when you have the ability to drop down to f/2.8, f/2, f/1.4, or even f/1.2, your shutter speed can remain high enough to ensure sharpness and clarity. This comes in especially handy in low-light situations: Where kit lens users (often stuck at f/4) will have to attach a flash, boost their ISO (and increase noise), or whip out a tripod, those with “fast glass” can drop down to f/2.8 or f/1.4 and continue shooting (to an extent).
Another use is to create a lovely “bokeh” behind your subject — points of light which become pretty ovals when out of focus. Lastly, it’s useful for shooting situations which require the fastest possible shutter speed, such as macro, sports, or wildlife, so a fast lens is necessary to ensure sharpness, focus, and clarity.
Don’t use for: Landscapes or any scene requiring overall sharpness.
Remember: When opening up to f/2.8, or especially f/1.8 or f/1.4, your focal area — where there is sharpness — becomes very, very small. Even on a face, you can have sharp eyes, but lose sharpness on the mouth or hair (which can look lovely when done creatively). You therefore need to be very accurate that you are nailing your focus on your subject (especially if a face). A portrait with one blurry eye is never a good thing. Another thing to note is that you can create extra blur / bokeh by putting distance between your subject and the background (the closer the background, the more in focus; the farther away, the less in focus).
Best lens: Depends on the end goal. If you’re into travel portraits — where sometimes there is a bit of distance between you and a subject — a fast lens with a bit of zoom is handy, such as 24mm-70mm f/2.8. If you’re really into intimate portraits, the 50mm f/1.8 or f/1.4 is beautiful on faces, though you will have to move your feet to get the right composition.
For shooting wildlife, you need both zoom and a fast aperture, so things start to get pricey. Still, if it’s your thing, a 70-200mm f/2.8 is the way to go (which is also good for travel / street portraits, but overall it’s best to ask rather than try to sneak a shot).

Numerical Solution to Ordinary Differential Equations

Ordinary differential equations (ODEs) are commonly encountered in scientific and engineering analysis. The simplest form of ODEs is the 1st order ODEs:

y' = f(y, x)

Here, y(x) is the function dependent on x, and it is the function that we want to solve for. X is the independent variable. The left hand side of the equation is the first order derivative of the function y, while the right hand side of the equation is a function that links the derivative to some combination of y and x. Function y is also known in ODEs as the solution function, while function f(y, x) is known as the flow function.

In generally, ODEs can be more than 1st order. It can be readily shown that, any ODEs (of any order) can be rewritten as a system of 1st order ODEs. Take the motion equation for the harmonic oscillator as an example:

x(t)'' = -k/m*x(t)

This equation can be rewritten as two 1st order ODEs:

 x' = F1(x,v,t) =v

v' = F2(x,v,t)=-k/m*x

Here, the harmonic oscillator 2nd order ODE is rewritten as a system of two 1st order ODEs, where there are two solution variables, x and v, two flow functions, F1 and F2, and one independent variable, t.

Numerical solutions to ODEs are readily achievable through discreet integration. The idea is that given an initial condition, i.e. y(x=x0), one can approximately compute the value of y at the next step, i.e. y(x=x0+h), assuming h is sufficiently small. The most straightforward solution is the Euler method. Takes the simplest, 1st order ODE as an example, at any given step, one can approximate the next step as:

y(n+1) = y(n) +h*f(y(n),x(n))

The essence of the Euler equation shown above is that, the next y value can be approximated by the current y value y(n), plus the step size times the derivative (slope) of the current x location, x(n). This is quite a crude estimation, because the derivative of y could change as x changes from x(n) to x(n+1). However, as a first order approximation, sometimes the Euler method is good enough, and its advantage is that it's easy to understand.

The Euler method can be easily extended to solve any ODEs with more than 1st order. As shown earlier, any ODE can be rewritten as a system of 1st order ODEs:

Y' = F(Y, x)

Here, vector notion is used to simplified the presentation of an ODE system. Y is a vector of all the solution variable in the system, while F is the vector of all the flow functions in the system. Therefore, Y is also known as the solution vector, while F is known as the flow vector. For example, in the harmonic oscillator example, Y=(x,v), and F=(F1(x, v, t), F2(x, v, t)).      

Applying the Euler method to an 1st ODE system is very similar to a single 1st order ODE:

Y(n+1) = Y(n) + h*F(Y(n), x(n))

Here, Y and F are both vector, while, h and x are scalar. The equation above in fact represents a set of equations. The vector notation is just to simplify the presentation of them. 

The disadvantage of the Euler method, despite its simplicity and intuitiveness, is that it's quite unstable, and tends to produce large error. In the next blog entry, we will introduce another method, the Runge-Kutter method, which is the work house for most of numerical analysis of ODEs.

Block comment and uncomment codes in VIM

In VIM, it is quite easy to comment/uncomment a block of lines.

To comment a block of lines:
a. Ctrl-V and mark the block of lines to be commented out;
b. shift-I and write the text that you want to prepend to each line, e.g. #
c. press escape.

To uncomment a block of lines:
a. Ctrl-V and go down vertically until the last commented line;
b. press x.