Depth-of-field considerations when choosing between a full-frame and reduced-frame digital SLR

Introduction

Main considerations when comparing full-frame and reduced frame digital SLRs typically lie in the areas of price, image quality and view-angle.

One often neglected area comparison is the depth-of-field that each camera would give.

The comparison here would be based on APS-C and 35mm, and the basis of comparison will be prime lenses of commonly available focal lengths and apertures.

The prime lenses used are as follows:
20 mm f/4.5
24 mm f/3.5
28 mm f/3.5
35 mm f/2.0
50 mm f/1.4
85 mm f/1.8
108 mm f/2.8
135 mm f/3.5
200 mm f/4.0


Comparison methodology

After visualising a scene, a photographer must select the appropriate focal length to cover the correct view angle. This focal length is dependent of the sensor size used. The focal length on a full frame camera is 1.6 times that of a APS-C camera to result in the same view.

For example, a 50mm lens on an APS-C camera will give the same view angle as an 80mm lens on a full frame camera.

Using idealised equations (which are suitable for use with prime lenses due to their reasonably simple optical design), the depth of field can be calculated when the sensor size, focal length, aperture, and subject distance is known.

In this simulated study, the following is assumed:
The photographer wants to capture an object 3m wide on camera. After putting on a lens, the photographer moves himself to a position so that the 3m object fills the frame. He then selects the largest aperture, and then observes the depth of field after taking the photograph.


The following correlation is used:

Where N is the aperture number, f is the focal length, s is the distance to subject, and c is the circle of confusion diameter. This correlation is applicable for moderate to large distances. [source]

Using this correlation for a full frame camera and 50mm f/1.4 lens, we adjust the subject distance to 4.3 m so that the 3m wide subject fills the frame. We then determine the depth of field (in this case it is 0.6 m). A 50mm lens on a full frame camera spans a horizontal view angle of 39°.

The result can be charted on a graph, where we compare view angle with depth of field.


Figure 1. The depth of field of various lenses when mounted to a 35mm camera, with aperture wide open and the subject distance adjusted such that a 3m wide object fills the frame.

The same exercise is repeated for the APS-C camera, and the data is plotted on the same chart for comparison.

We see that the view angle for the lenses are narrower, which is not surprising since the APS-C sensor is smaller and thus sees a narrower field. A correlation between the view angles of full frame and reduced-frame cameras is as follows:

When mounted on a reduced frame camera, the view angle is the same as a lens 1.6 times longer mounted on a full frame camera. For example, the view of a 50mm lens on an APS-C camera is equivalent to that of a 80mm lens on a full frame camera.


Figure 2. The depth of field of various lenses when mounted to a 35mm camera and an APS-C camera, with aperture set to wide open and the subject distance adjusted such that a 3m wide object fills the frame.

More importantly, the depth of field becomes wider when using a reduced frame camera. This is the case through the entire range of lenses, except at 85mm, where an 85mm lens on a reduced frame will out-bokeh a 135 mm lens on a full frame camera. Incidentally, the view from these two set-ups are equivalent. A 85mm on APS-C looks like a 136mm on full frame (85 x 1.6 = 136).


Conclusion

Depth of field at any specific view angle is dependent on both the view angle and aperture size. Using a system of inter-changeable lenses on both full frame and reduced frame cameras, the full frame camera consistently results in a narrower depth of field, aiding the application of bokeh.

You cannot hide from The Internet - part II

This is a continuation of the narration that started here.


Prologue

Some time in the recent past, a mysterious woman's name started appeared in several semi-private documents. Her inclusion had been a subtle one, not more than a droplet in a raging torrent of information.

By a stroke of misfortune, her presence was noted by a very observant sentinel. The sentinel quickly alerted her colleagues, and a search immediately started.

She had relied on hiding among the many other data sets to veil her presence. With no encryption nor disguise, once an active search began she was quickly and easily found by following her vast network of paper trails and digital footprints...

***
“And how is your mother coping with this?” he asked her, squinting his eyes against the morning sun. They had just rounded a corner – a tight 2nd gear curve with a bit of camber – and when they received the full power of the 8am sun in the clear, cloudless sky.

“She's quite ok, I think. The change of environment will be good for her,” she replied, absently looking out of the window as the scenery sped past them.

He slowed the car for another curve, this time a left-hander. Easing off the brakes, he nudged the car's nose inwards. After the mid-point of the corner, he gradually unwinds the steering wheel and opened the throttle.

“Oh, did you see the latest updates this morning?” she asked after a bit of silence. “She went to Hong Kong.”

“Who?” he asked unthinkingly. He was concentrating on slipping the car through the curves as smoothly and quickly as possible.

“Tiff.”

On hearing her name, he instantly returned to reality. “Did our man go along?”

“No, don't think so.”




Soon, they stopped at a coffee shop for breakfast, an old establishment that came up in the post-war years. The kind that still retain the quaint original wood and marble tables and where retired gentlemen come for long breakfasts.

They shared a charcoal-toasted kaya and butter sandwich, two soft-boiled eggs with a dash of soy sauce, a light fluffy steamed red bean bun, and had a cup of strong thick coffee each.

Satisfied with their meal, he checked the vicinity for wireless connections. Finding a publicly accessible connection he reached into The Internet to plumb for information.


“Ah, I see what you mean by Hong Kong now,” he remarked.
“Yes, if you look through the records you can see who she went with.”
“I'm sifting through the details of her friend Charmaine on Facebook [link].”
“Mm.”
He gasped abruptly, “Charmaine knows Jill's brother! Photograph here [link]”
“Good. You find out more from Jill.”
“She's not online now.”
“Do it later. But I just want to know three things. One – Tiff's character. Two – is she smart. Three – what business is her family in. After that you can ask anything you want; I just want three answers.”
“Very well.”


There was not much of else great importance, and they disassociated themselves from The Internet in preparation to leave.


“I still find it odd. Why Tiff? She's so young... Well she better be smart damn it!”
“Mm, we'll see.”

LDR

Had briefly contemplated naming this "In Search of The One" or something similarly dramatic, but that would be pushing things a bit. Thus this spawn of Photoshop shall remain untitled like an unnamed offspring from an illicit affair.

***

I rarely dream, but yesterday I dreamt that I was peeing.

The liquid that came out of my urinary tract was black in colour, like diluted ink.

Deriving the present value of a fixed-payment annuity of finite life (not a perpetuity)

Many finance text books will provide the formula for the present value of such an annuity as the following:

Where C is the payment made every period, r is the discount rate to be applied, and n is the number of periods.

Unfortunately, elementary finance text books have a distasteful habit of presenting equations with no proof. The reader can either believe it, or sod it.

Here, we will derive the above equation.


The present value of an annuity is the sum of the discounted payments, as follows.

This sum can be expressed as the difference between two infinite sums (perpetuities) starting at different times:

Notice that the second perpetuity starts at n+1. We then modify the second perpetuity's notation so that the index starts from 1:

From studies of the present value of perpetuities, we know that the following is true:
*The derivation of this is attached as an appendix.

Substituting the above equation into our present value of an annuity:



Appendix – deriving the present value of a perpetuity

A perpetuity is an endless stream of fixed payments occurring at fixed intervals.

Its present value can be computed as follows:

The value of the infinite sum can be expressed as follows:
For simplicity, 1+r is replaced with x.

When we replace x back with 1+r, the equation becomes

Substituting our result into the present value of a perpetuity:

Wedding planning

I was chatting with May some days ago when the topic of weddings crept up. We started talking about what we will do for each other's wedding, at what age will marriage be appropriate, etc etc.

Not surprisingly, I have been drafted into the photography service for her future wedding.

May: when u get married i wanna be wedding planner ok
get big ang pau!!!!
then u no need to be stressed
coz u won't know what colour to chose
u will only select the lighting!
“i want all yellow light..”
haha
then hotel have to change all the bulbs
Me: pfft
no, i want diffuse light
shine from the bottom onto the ceiling
reflect off the ceiling
yah.. whatever light la..
then light cost more than the food
That, would be the best wedding
ever
wtf
lol..
then ur wife tiew [will fuck you]
haha

[...]

May: i think i will get married about 30 la..
how about u?
Me: dunno err
30 is probably a good age
but as long as its with a suitable person, the age is not a problem
how old are u?
2 years older than you
how old are you again?
22
means u 24
ok..
30 is probably ok u la..
ya meh im 24?
no i'm 25 this year
wtf i kena con d is it
its 2008
i was born in 83
im 25 lah stop confusing me wtf
haaha
WOI!
u mean u need to question ur self and anaylse?
you know i forget, dont exploit me ok!
wtf ?
i need to count years
wtf man
u need to think and calculate?
yeerrrrrr
u make me laugh untill wanna pang sai
i go shit 1st
hahaha
wtf
go go you're full of shit :P

No I'm not getting married anytime soon, don't ask.

There is light at the end of the tunnel

I just hope the tunnel is not too long.

Faber-Castell

Faber-Castell

Click here for large size image
Super-Takumar 50mm/1.4


One of my best photographs in a while; I'm quite happy with it.

Bureaucratic misadventures when obtaining a work permit in Tianjin, China

Assume that:

• you are in China on a tourist visa, and
• you have a 30-day tourist visa, and
• you have received an employment offer from a Tianjin firm.

After fumbling about, you find out the general structure of the application process:

• Apply for a license for a working visa
• Apply for an notification letter to allow a working visa
• Return to Kuala Lumpur, and apply for a 30-day working visa using the aforementioned license and approval document
• Upon entry to China, apply for a work permit
• Using the work permit, apply for a residence permit so that you can stay for more than 30 days

License for application of working visa

To obtain this license, you need to get a medical examination from the immigration department's hospital.
Hence you go to the immigration department's hospital. They tell you that you need a license for application of working visa before they can give you a medical examination. WTF.

Oh shit, a paradox. A snake eating its own tail. A perpetual motion machine.

You whine rant to your manager. The manager talks to a few people, and the immigration's hospital agrees to allow you to be given a medical examination despite not having a license of application of working visa.

You do your medical examination, and complete the paperwork.

5 working days after the submission, you get the coveted license for application of working visa. You have now levelled up- you are allowed to apply for a working visa, yay!



Notification letter to allow a working visa

Of course, the embassy will not flippantly approve working visa applications lest China suffers an influx of talented professionals.

So the embassy will require a formal notice from the province government before they will approve a visa application.

To apply for this notification letter, you will need to go to the Labour and Public Security Bureau with some forms you printed from the department's website. There, a surly looking woman will tell you that you need to get approval from the city/town government office before coming to the province level department.

You need to fill up the form on their website, and submit it. Wait for one working day while someone at the other end of the line proofreads your submission. Upon approval, download the completed form and print it out. Bring the form and supporting documents to the city/town labour department for their approval.

They will slyly tell you that you actually need photocopies of documents that were not specified, thus requiring you to make another trip.

After the stamp is obtained, you can now apply for a notification letter to allow a working visa.

You bring the stamped form back to the provincial-level Labour and Public Security Bureau, where the surly looking woman has changed to a slightly pleasant lady. She will tell you the network is down, so please come back tomorrow. Tell her you'd wait a while in hopes the network is restored.

The network gets restored, and you apply for your notification letter. She prints out a formal looking document for you.

Congratulations, your future application for a Working Visa will have a higher chance of getting approved!



Visa applications

You return to Kuala Lumpur to apply for a working visa. One of the important considerations is that you have sufficient assets to show that you will not starve. The minimum balance in your bank account is to be RM 3000.

You ought to be pissed off now. So, the best thing you can do is to find the account with the biggest balance. Your Public Mutual investments have RM [omitted] in them, but you cannot get the balance sheet in the blink of an eye. So look for your BT Investments' online balance sheet, and show them the AU$ [omitted] you have in there.

You hand over the required documents to the embassy 2 weeks in advance. Curiously, they ask you when you will be flying into China. You tell them the 14th of June.

The embassy bounces the application back at you.

“Too early,” they say, “come back in 4 days time.”

Curse at them, but do not neglect to swear at their grandmothers as well.

When you finally get your working visa, check the validity period. It will be invalid on 15th of June, one day after your estimated entry to China. Hence you cannot change your flight.

This time, swear at their grandfathers.



Entry to China

Upon entry to China, you need to register yourself with the local police. Bring your passport, a photograph, your residential rental agreement, and a photocopy of the landlord's identity card. The police will issue a foreigner residence registration document.



Applying for a work permit

Bring your passport, employment contract, foreigner residence registration document and medical examination results to the Tianjin Human Resource Bureau.

One week after submission, pay the processing fee of 600 Yuan and then collect the work permit.



Applying for a residence permit

The working visa only allows you to stay for 30 days, thus you need to apply for a residence permit to extend the period to 1 year.

Go to the provincial Immigration Department, find the relevant form and fill it up. Queue up at the counters, noting the slow pace of work.

When you see an officer, she will tell you that you need to get photographs taken at their photograph booth because they need the electronic copy, and then go for an interview with an officer, then come back to submit your application.

This is another good time to be pissed off.

Queue up to pay for the photograph's fee of 50 Yuan, noting the counter attendant's bored and can't-be-fucked look. (aside: he literally cannot be fucked- anyone trying to get boned by him will be immediately turned off and lose all sex drive) Get your mugshot taken, collect the prints and then queue up outside Room 103. The area outside Room 103 is an unmistakably dingy corner located next to the toilets.

The officer in Room 103 will have a quick discussion with you. Satisfied that you are not a terrorist and you have valid reasons for entry, he sign an approval form for you.

Take this document (and the photographs) to the application counter and queue up. When it's your turn, remember to submit the documents.

Return to the Immigration Department in one week, pay 800 Yuan and you have completed your quest to work in Tianjin.

Now you will ask yourself, “why am I working in China?”

You cannot hide from The Internet

It was a dark stormy night when her name was noticed in the lists.

Outside, gusts of howling wind drove the rain streaks in diagonal slashes, impinging upon glass facades with stout, firm thuds. The black sky would occasionally erupt in flashes of lightning, bright enough to illuminate the entire city for milliseconds. Thunder would follow in several seconds.

Indoors, the occupants couldn't care less. They had air conditioning that removed moisture from the air; they use computers, not windows, to see the world; with adequate surge protection and uninterrupted power supply.


“Who is she?”
“We don't know.”


At once, three minds reached out to Google.


“I have her blog.”
“I see it, but the address has been taken by someone else.”
“Friendster profile [link]. It's a private profile though.”
“She's connected to Chin. I'll ask Chin about her the next time I see her.”
“I think Joanne might know her.”
“Why?”
“She is either in PWC or Daimler-Chrysler. She is connected to someone who consulted both firms.”
“Ok, she's most probably from PWC. She knows Victor, Ling and Joanne – all of them PWC people.”


Satisfied they have enough of a lead for further investigation, the three withdrew their enquiring tentacles from The Internet.


“A bit young to be playing in such deep waters, don't you think?”
“Mm, we'll see.”

M&Ms

I should be studying Corporate Finance and Portfolio Management.

Eating M&Ms while studying is perfectly acceptable (and encouraged); playing with M&M's instead of studying is frowned upon.




Dead Pixel

Toshiba webcam, 0.3 megapixels
Webcam contributed by May



These M&Ms were arranged in the same way cathode ray tube monitors' pixel elements. In reality, CRTs do not suffer from dead pixels; only LCD monitors exhibit dead pixels.

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