Forward Bias Photodiode circuit
I'll edit this answer severely as a general comment:

Photodiodes may be operated either forward or reverse biased. 


Forward biased gives most output.  
Reverse biased gives most speed. and is noisier.
In this mode Vsupply needs to be &lt; Vreversebreakdown - hopefully in the data sheet.


Reverse biased mode is most usually used.

The Sharp BS120  is optimised for 560 nM operation. It specifies Vreverse_abs_max as 10 volts and has curves all the way up (or down) to -10V.



Wikipedia says



In "forward biased" mode the diode is usually operated with NO added bias and is used as a voltage source.

For a silicon diode with Vforwards = Vf = 0.6V  . 
Say you want 5 mA current and are using a 5V supply  then

I = V / R =  = (Vsupply - Vdiode) / R = (5-0.6) / 0.005 = 880 ohms
 Say 1000 Ohms (which gives a notional 4.4 mA)

For 1 mA you'd use (5-0.6)/0.001 = 4400 Ohms