In this paper we define an operator measure s on L(X) into R⁺ {0} satisfying suitable conditions. Then letting I = s⁻¹(0), we consider the quotient algebra L(X)/I, instead of Calkin algebra and define α₁(T) = {λΠ₂(λ−T) is not invertible in L(X)/I where Π₂: L(X) → L(X)/I is the natural homomorphism, and r₁(T) = sup{¦λ¦:λ ε σ₁(T)}. After proving the fact that σ₁(T) is equal to the essential spectrum of T and replacing standard measure of noncompactness with suitably defined s-measures we obtain that the radius r_e(T) of the essential spectrum is equal to lim_n(s(Tⁿ))^1/n. We also construct examples of such operator measures.