p be an integer when 8 n p 1 u2267 y x u2267 8 n p with 3 u2267 p u2267 0 ph3 p 1 when 8 n p 1 u2267 y x u2267 8 n p with 6 u2267 p gt 4 ph3 p 2 when 8 n p 1 u2267 y x u2267 8 n p with 10 u2267 p u2267 7 ph3 p 3 when 8 n p 1 u2267 y x u2267 8 n p with 15 u2267 p u2267 11 ph3 p 4 it should be mentioned that this set of relations is used to obtain the phase approximate value within 7 13 degrees the coordinate ratio inequalities are not fixed and can be properly modified according to the phase resolution n from the above described relations one sees that when n 1024 the relations can be shown in tables 1 and 2 it should be mentioned that if the phase u03b8 generated by the disclosed phase detection device is not expressed in terms of 10 bits the value of phase resolution n also changes the first phase approximate value ph1 the second phase approximate value ph2 the third phase approximate value ph3 and the coordinate ratio inequality within 7 13 degrees are also adjusted accordingly furthermore fig5 shows the detailed steps.