Change the integration variable x to xdh=x/h , in this way parameter h dissappears

eq = ArcTan[1/d*Sqrt[(a + b)/(1 - b)]] - (Vi/h)*Integrate[Sqrt[(1 + (xdh)^2)^(-1)], {xdh,(1/2)*Log[b], 0}] h + (Pi/4) +m*Pi

ConturPlot shows possible real solutions {Vi,b}

pic=ContourPlot[0 == eq, {Vi, .8, 5}, {b, 0.0, .6}, FrameLabel -> {Vi, b}]

List of solutions found:

pic[[1, 1]][[1]]
(*{{0.8, 0.0416416},{0.804065,0.0422764}, 
{0.807732,0.0428571}, {0.8375,0.0477974}, 
{0.838872, 0.0480182},...}*)

Change the integration variable x to xdh=x/h , in this way parameter h dissappears

eq = ArcTan[1/d*Sqrt[(a + b)/(1 - b)]] - (Vi/h)*Integrate[Sqrt[(1 + (xdh)^2)^(-1)], {xdh,(1/2)*Log[b], 0}] h + (Pi/4) +m*Pi

ConturPlot shows possible real solutions {Vi,b}

pic=ContourPlot[0 == eq, {Vi, .8, 5}, {b, 0.0, .6}, FrameLabel -> {Vi, b}]

List of solutions found:

pic[[1, 1]][[1]]
(*{{0.8, 0.0416416},{0.804065,0.0422764}, 
{0.807732,0.0428571}, {0.8375,0.0477974}, 
{0.838872, 0.0480182},...}*)

Alternatively try direct solution NSolve

sol[Vi_] := {Vi, b} /. NSolve[{0 ==eq[[1]], 0 < b < 1}, b][[1]]   
Table[sol[Vi], {Vi, .8, 5, .1}]  

Change the integration variable x to xdh=x/h

eq = ArcTan[1/d*Sqrt[(a + b)/(1 - b)]] - (Vi/h)*Integrate[Sqrt[(1 + (xdh)^2)^(-1)], {xdh,(1/2)*Log[b], 0}] h + (Pi/4) +m*Pi

ConturPlot shows possible real solutions {Vi,b}

ContourPlot[0 == eq, {Vi, .8, 5}, {b, 0.0, .6}, FrameLabel -> {Vi, b}]

Change the integration variable x to xdh=x/h , in this way parameter h dissappears

eq = ArcTan[1/d*Sqrt[(a + b)/(1 - b)]] - (Vi/h)*Integrate[Sqrt[(1 + (xdh)^2)^(-1)], {xdh,(1/2)*Log[b], 0}] h + (Pi/4) +m*Pi

ConturPlot shows possible real solutions {Vi,b}

pic=ContourPlot[0 == eq, {Vi, .8, 5}, {b, 0.0, .6}, FrameLabel -> {Vi, b}]

List of solutions found:

pic[[1, 1]][[1]]
(*{{0.8, 0.0416416},{0.804065,0.0422764}, 
{0.807732,0.0428571}, {0.8375,0.0477974}, 
{0.838872, 0.0480182},...}*)